I recall that a shichibukai needs to have quite a good bounty, and be very strong. So why was Luffy never offered the position? I mean his second bounty was higher than Crocodile and Hancock, so if we say he offended the World Government in the Enies Lobby arc, then before that, he was eligible, and even afterwards, we can't say he's not eligible; let's not forget Doflamingo threatened tenrybito with revealing some information, and his status was not revoked.
So why not?
First time around when Luffy took down Croc, BB offered to take the position of Shichibukai by presenting the marines with Ace. It was an offer the Marines could not pass up on, so they did not think of any other suitable candidates.
Also, since the credit for taking down Croc was given to Smoker, Luffy was relatively unknown. This further emphasized the reason as to why he was not considered because Shichibukais would generally be selected from feared and notorious pirates.
After the war of best, there were three vacant positions for the Shichibukai. But none of them were offered to Luffy. This is because Luffy by then has declared war against them by burning the flag of WG. He attacked Ennis Lobby, Impel Down and Marineford the three symbols of the Marines, he punched a Celestial Dragon and he rung the Ox bell 16 times which declared the coming of a new age of pirates. All this made Luffy as someone who would be an enemy to the world government not some random pirate like the other Shichibukais who were even though notorious pirates did not directly meddle with the affairs of the World Government.
This is the reason he was not offered the position.
Also considering Luffy, like Ace he would have never accepted that position because that would limit his freedom.
Because Blackbeard made a deal that he'd bring them Luffy's head to become a warlord. By the time Blackbeard had renounced his position, Luffy had already declared war on the world government, defeated another warlord, destroyed their judicial island, led a mass prison break from their prison island, and partook in a war against the government at the marines's headquarters, punched a world noble, and completely defeated their secret assassination squad CP-9. By that point, they didn't want anything to do with him besides bringing him to justice. Now they even revoked Law's status just for allying with him.
Well, for starters, despite being eligible for the position, he gained that meaty bounty after defeating a former Shichibukai, and while that may qualify him for the position, Luffy also thwarted Operation Utopia, which was covered up by the World Government to give the credit to Smoker and hide the fact that the whole Shichibukai system is flawed and prone to abuse. Luffy becoming a Shichibukai would make the public question what deeds he had done in order to earn the position, and may expose the truth that it was a pirate that saved Alabasta, not the Marines. Also, while it is the World Government's decision, I doubt the Marines will agree with the decision of making Luffy a Warlord post-Alabasta, especially Smoker.
One answer can also be that the World Government considers all D's as the enemy of world government or just the fact that luffy is the son of Dragon is enough reason to not to make luffy their ally by making him a Warlord.
The Shichibukai position isn't tied to bounty or even personal strength, it's tied to influence. Mihawk and Crocodile were given the position despite their low bounties because they had become well known around the world by then. Hancock was also offered the position at a fairly low bounty because of how early she became famous and because the World Government didn't want to make enemies with the Amazons and Buggy was given the position after Marineford due to his influence on other Pirates.
The Shichibukai have to be well known and respected or even feared as it is their responsibility to hunt other pirates. Luffy was largely unknown for quite some time, not really being a respected name until after Marineford by which he had already crossed the World Government thrice over.
Well, here's my theory. I think the fact that Luffy is the son of the most wanted man on the planet "Monkey D. Dragon" is enough to stop them from making him Sichibukai.
Secondly, if there's a once-in-a-blue-moon chance that they had offered him to become a Sichibukai, then without any doubts Luffy would've refused it because he does not want to work under someone. Otherwise, he would have taken Ace's advice to become White Beard's crew member.
The Gorosei and the heads of the Navy know who Luffy is. Even when the rest of the world thought Smoker did everything, the Gorosei/Navy knew the truth. They even knew things that he didn't, like, the fact that his father was Monkey D. Dragon.
Garp knows that Luffy carries that same spirit in him, hence all the love fisting. He was close with Sengoku, and if he thought Luffy would do it, he definitely would of spoken up, but Luffy always told Garp "I want to be a Pirate, no Navy".
The Gorosei wouldn't want him anyway, due to the true purpose of the 7 Warlords, which is to do all the underhanded and sneaky crap the Navy can't be caught doing. They know if Luffy ever got a hold of the info they are hiding from the public, he would stop that immediately. Not that Luffy would figure anything out, but, once Nico Robin explains it to him, well you get the picture.
So, basically, he wouldn't do it and they don't want to ask him. Especially since Sakazuki is Fleet Admiral now. That dude is a whack-a-do who killed his bro.
Luffy's goal isn't having a position like a king, leader, or a Shichibukai.... cause he doesn't want to be controlled, he wants to have fun, great adventure, exploring, and things like that, that's why he is so close to the Red Hair Crew. When Luffy was a kid, they came and told him stories of their adventures, so that being a pirate for him is the meaning of freedom, he even refused being the boss of the grand fleet (chapter 800). As he said "I wanna be the pirate king not an important person".
