King is many times referred to as the strongest man alive and the Hero Association stats give him a ranking of 10 in everything: Stamina, Intelligence, Justice, Endurance, Power, Popularity, Effectiveness and Fighting Ability. So, if they think he's perfect and the strongest hero, why didn't they rank him higher than #6?
Adding onto @Gary Andrews30, the reason that King wasn't ranked any higher was because of the simply outstanding heroes ahead of him.
.6. Bofoi (aka Metal Knight), he helped create the newer Hero Association and he literally has the skills to manage extremely advanced technology. And as Gary said above, rank isn't determined by strength, they look at other things. King has almost never responded to his hero calls (calls for help by the hero association) and only comes when there are the biggest of crises (ie. Monster Association) and that was only due to Saitama coming along. However, since Bofoi doesn't respond much either, the deciding factor would probably be the contribution to the Hero Association. As mentioned before, Bofoi helped construct the new Hero Association building, while King hasn't done much in that retrospect(This isn't backed by much evidence because Bofoi doesn't have much character time and indications).
.5. Child Emporer, his overall skills include extreme intelligence and technological mastery. He is most likely not as skilled as Metal Knight, but a possible factor could be his willingness to help out the Hero Association and his strategic leadership as shown when he led the S rank heroes into the Monster Association. Therefore, because of his active participation vs King's declination of emergency calls, Child Emporer is ranked higher than King.
.4. Kamikaze (Atomic Samurai), need I explain this one? Although mentioned in the Webcomics that
Kamikaze believed that King cut the apple (a test of strength) so fast that the molecules rejoined
However, as readers, we obviously know that King if actually faking and doesn't know what he is doing. However, Kamikaze has connections and pupils, which makes him viable and due to his immense prowess in katanas he is considered extremely dangerous and powerful. His pupils that are A rank 2, 3, and 4 (remember, A class high rankings are already considered powerful) contribute with Atomic Samurai and if Atomic Samurai, the proud Samurai he is, happens to dislike something or is displeased with his rank, the Hero Association would most likely lose his pupils along with a great warrior. Not only that but Atomic Samurai also has connections with other sword dojos as shown when they meet up and discover that one of them had been monsterfied with the monster hearts. One of the Masters mentioned "I will mobilize my pupils", so notice the plural of the word "pupils". This means that because Atomic Samurai already carries influence among the top-ranked A heroes and also has other sword dojos backing him up, the Hero Association could not afford to lose someone like him. Compared to King, Atomic Samurai holds to much influence and power/skill to be ranked lower.
.3. Bang (Silver Fang) Simple, Bang is wise. He recognized Saitama's power right away and even mentions that Saitama is more powerful then him. Bang also has mastered one of the most deadly martial arts techniques, Fist of the Flowing Water Crushing Rock. (Just take Garou as an example). Moreover, Bang always showed up, no matter what happened. For example, at the start of the series when a meteor was falling, only Bang, Genos, and later on Metal Knight and Saitama showed up. Bang calmly, calmly looked at the meteor that could literally destroy him and just chilled. Genos, the Demon Cyborg only came because he was worried about master Saitama being bothered by the meteor. ( I assume that he would've just yeeted outta there if Saitama wasn't there), and Bofoi (Metal Knight) only went to test new technology. So not only does Band cough responds to the calls, no matter how dire they are, but he also uses an extremely powerful martial arts technique that not many people can withstand.
.2. Tatsumaki (Terrible Tornado) Tatsmuaki doesn't really need to be explained. Yes I do realize that she doesn't respond to calls much either, but she is just simply too strong. My theory is that if she can float, how would the "Strongest Man on Earth" even touch her? We have never seen King's feet leave the ground (Just gonna assume that King can't fly or levitate). So based on that, Tatsumaki simply overpowers the "Strongest Man on Earth", not based on physical prowess, but by psychic raw strength.
.1.Blast Not much is known about Blast even int he Webcomics, but there are many theories that I won't explain because of lack of evidence. However, he has been described as, "Fubuki mentions that Blast is "the one at the top of all heroes" during her talk with Saitama in his apartment, putting Blast alongside King in terms of power."
Buuuut we all know how powerful King really is right....? Wait, you're telling me that after spending ~1 hour writing this that King actually is the strongest? WDYM? ~~~~~ ~~~~~~ _________
King Cares Naught For Such Baubles
King doesn't really want these things, and the attention has become more than he can handle. He was too shy and awkward to tell people they were wrong (and possibly very early on they still would have already dismissed this as his being supremely humble, and not an honest admission of factual weakness), then it was kind of convenient, then he didn't want to let people down, and now he's terrified of what would happen to him if people found out the truth.
As such he will make no demands for an elevated position, and may express an active dislike of the idea of a promotion. In the latter case, who would dare to anger King by giving him something he has rejected? In the former they may surmise he has neither need nor desire for higher accolades or bragging rights, and so they can use the higher rankings as incentives and rewards for those heroes more concerned with such things. Bang is about the only one of a higher rank who this doesn't seem to apply to, but everyone else in the top 6 (and much of the rest of the S-class) seems pretty arrogant and convinced of their total superiority, and desires to be recognized as such.
As Sphinx mentioned, while King's rated as a 10/10 on Effectiveness, he's not very reliable to the Hero's Association as a go-to problem solver. King is believed to be an unbeatable killing machine, but he almost always operates according to his own whims and desires. But it's being a go-to problem solver that really moves you up into those top ranks.
And that's where you see King outshone by the top 6 (well, 2-6 at least). (A similar rundown to the following exists in Sphinx's answer)
Blast (rank 1): He's mostly like King in his (alleged) supreme power and aloofness, but he is considered to be 100% reliable to answer a call to resolve a truly world threatening crisis. Sitch seems to have an almost religious faith in this.
Atomic Samurai (rank 4): He quickly surmises that Bang may have difficulties diffusing the Garou situation due to his emotional attachments. He then moves to solve that problem, and when he learns of the Monster Association he quickly moves to deal with that. He also has very potent underlings within the Hero Association—I think someone, maybe Fubuki, says that his three apprentices may already be at S-class level, and are only stopped from being such by Sweet Mask. So we know he responds quickly to threats to the HA, and essentially controls three of the four most powerful known A-class members. That makes him a great asset to the organization itself.
Bofoi/Metal Knight (rank 6): Most of the HA's technology is due to Bofoi, including the new and old headquarters. His ability to remotely pilot powerful mech suits, possibly several at a time, grants him immense versatility to solve a wide variety of issues. He does, however, seem pretty selective in what he'll actually bother with. However, the technology and construction alone is an incredible asset and service to the association, and he's proven very reliable on that.
Child Emperor (rank 5): Turns out he's a former student of Dr. Bofoi's. He has a similar profound gift for technology. He is constantly trying to innovate new devices to assist the Hero's Association, and during the Monster Association arc he shows a lot of leadership and initiative. Presumably the HA had already seen such behaviors from him, making him very valuable.
Bang (rank 3): The wise old martial arts master. He is probably already invaluable simply from being able to diffuse Tatsumaki's temper on occasion. He is a seasoned teacher, guide, and trainer who does not seem to have any issues with responding to calls to action.
Tatsumaki (rank 2): While Blast is considered the sure bet policy against worldwide threats, Blast is not the person the association truly relies on. Their true insurance policy, that they can always fall back on to crush any threat, is Tatsumaki. While she is immensely arrogant, do note how we see her several times complaining about how they're sending out some other hero when she could do it herself; she has remarked that she finds all other heroes (except Blast, and sort of King) useless in comparison to her, and that she could do it all herself. The association specifically calls on her to take out the giant dinosaur monster guy, too. So while she is difficult personality-wise, she is immensely versatile and immensely reliable at solving problems sent her way, and even eager to solve more of them. The HA can expect her to deal with anything they ask her to deal with, and that she will succeed.
The Hero Association was founded several years ago. It is implied that it was founded by the father of the child Saitama saves from Crablante, as a response to that event, in fact (this is just before Saitama trains to be a hero). The S-class did not originally exist then, but at some unspecified point the HA became aware of a certain group of generally low-ranked heroes that would routinely devastate monsters that had in turned devastated the upper ranks of the association. The S-class was made to acknowledge such heroes and make sure their talents weren't lost to the association. Presumably the S-class has been around for two years or so now. Saitama, however, hasn't been operating as a hero that long. The story starts not long after he's completed his three years of training; just long enough to begin suffering ennui from being so overpowered. As such, the S-class may have already existed before King started inadvertently getting credit for Saitama's actions. King would then be the relative newcomer, and rising to the formal #1 (or #2) position in a short span could be problematic, bureaucratically or otherwise, and so impeded.
We've also seen with Saitama that, even with the effective endorsement of multiple S-class members (Bang, Genos, and King with what's already been shown in the anime) that he is (above) S-class in power, he still wasn't jumped to the top of the ladder. His advancement has in fact been considered very rapid, and he's still not even been put into the top of A-class yet.
The main problem with this bit is that we've received a few bonus chapters about Saitama's training days, wherein he was already one-shotting monsters before a year was up, and taking out monsters too powerful for multiple A-class heroes to deal with in a single absent-minded attack before he's lost his hair, as well. So Saitama was in fact leaving a trail of unclaimed monster kills behind him for years. However, since he wasn't actively trying to deal with any of the monsters in these stories perhaps they were rare occurrences. The unlucky monster that crossed his path during his 10km run may be all he dealt with.
While the story doesn't spend much time directly trying to say it, a lot of the previously mentioned slow advance is meant to underscore a certain amount of inefficiency, bureaucratic red tape, inadequate tracking and power measurements, and even outright corruption that taints the operations of the Hero's Association. It's a for-profit non-governmental organization that largely caters to the whims and demands of its biggest donors. Much of the system is built around cults of popularity, with heroes judged on the coolness of their outfit and backstories, rather than their actual capabilities and achievements. Nothing is done to stop newbie crushing and "camp sitters" like Fubuki and Sweet Mask. The S-class became necessary because of systemic failures to recognize the actually effective and powerful people who flew under the radar because they didn't care about these things, while those obsessed with their popularity stood at the top but yet proved unable to handle the biggest threats. The issues with its ranking system are just symptoms of the greater disease.
This has become a plot point in the webcomic, as many heroes, including S-class heroes, have now left the HA in favor of a new hero organization, and public perception of the HA has soured significantly (even before the departures).