Let's analyze this using protagonist of some Japanese light novels. Let's start with those you mentioned in the question. I'm excluding Basara of Shinmai since I don't watch the anime nor read the LN. I don't know him enough to talk about him. Also to be noted that I only write based on LNs that I have read, and I write their names using the natural writing order, not the Englished version.
Let me say beforehand, loner is not the same as social outcast.
High School DxD - Hyoudo Issei
Even at the start of the LN, Hyoudo Issei was depicted not as a loner. He has 2 close friends, Matsuda and Motohama, who are both as perverted as he is.
Yahari Ore no Seishun Love Comedy ga Machigatteiru (Oregairu) - Hachigaya Hachiman
He started the story as a loner. But, it was later revealed that he actually have 1 close (enough) friend, Zaimokuza Yoshiteru.
Sword Art Online - Kirigaya Kazuto (Kirito)
At the start of the LN, no friends of Kirito was mentioned. The story started with Kirito login in into the game, Sword Art Online where he met Klein and then was trapped along with other 6,000 players in a death game.
Oda Nobuna no Yabou - Sagara Yoshiharu
No friend of him was mentioned since he was sent into the other world mysteriously. But in the other world, he quickly befriends old man Tokichiro. He also befriends other characters as the story progress on.
Tokyo Ravens - Tsuchimikado Harutora
Harutora has a childhood friend who is also his cousin, Tsuchimikado Natsumi. He was also childhood friends with Kurahashi Kyouko, a distance relative. At the start of the story he was friends with Hokuto and Ato Touji.
Infinite Stratos - Orimura Ichika
No friends prior to him attending IS Academy was mentioned at the start of the story. However, it was later revealed that he actually has one close friend, Gotanda Dan. He also gets along with Dan's little sister, Gotanda Ran. He is also friends with Huang Lingyin and Shinonono Houki prior to the start of the story.
Date a Live - Itsuka Shidou
Itsuka Shido has one close friend, Tonomachi Hiroto.
Madan no Ou to Vanadis - Tigrevurmud Vorn
The only known friend of Tigre prior to the start of the story is his childhood friend and maid, Titta.
Rokka no Yuusha - Adlet Mayer
Adlet has no friends prior to the start of the story.
Boku ha Tomodachi ga Sukunai (Haganai) - Hasegawa Kodaka
Kodaka has 1 close friend prior to the start of the story, Taka.
Okay, I think this much is enough for examples. Let's start analyzing them. Of the ten examples I give there,
- 2 person starts the story with 3 friends, Orimura Ichika, and Tsuchimikado Harutora.
- 1 person starts the story with 2 friends, Hyoudo Issei.
- 4 person starts the story with 1 friends, Hachigaya Hachiman, Itsuka Shidou, Tigrevurmud Vorn, and Hasegawa Kodaka
- 3 person starts the story with 0 friends, Kirito, Sagara Yoshiharu, and Adlet Mayer.
I count Tsuchimikado Harutora as a person with 3 friends (Tsuchimikado Natsumi, Ato Touji, and Hokuto) as Kurahashi Kyouko was no longer his friend at the start of the story since he forget about her.
Merriam Webster defined loner as a person who is often alone or who likes to be alone. Dictionary.com defined it as a person who is or prefers to be alone, especially one who avoids the company of others. Wikipedia defined it as a person who avoids or does not actively seek human interaction.
The only one who really fit the definitions above is Hachigaya Hachiman. The other doesn't avoid company of others.
If we go with Merrriam Webster's first part of the definition, then Adlet, Kirito, and Kodaka also can be called loner. However, there are circumstances behind their lonerism.
Adlet was training in a secluded area where there are only him and his master. It was shown in the story that Adlet doesn't avoid social interactions.
Kirito's school friends was not depicted in the story because they have no relevance to the story. Kirito later was alone
since he took the blame after the boss killed some of the front liners and was called Beater. he did this to protect the other Beta Testers.
There is a circumstance behind him being alone.
Kodaka doesn't avoid company of others, in fact he longed for the company of others. It's just that his hair color makes him mistaken as being a yankee.
Orimura Ichika, Hyoudo Issei, Itsuka Shidou, and Tigrevurmud Vorn can't be called loner since they clearly have friends and they also doesn't avoid social interactions. While Sagara Yoshiharu doesn't start with friends, his behavior doesn't suggest that he is a loner.
Out of the 10 examples, only 1 was a true loner, that is 10%.
Does them being a loner also means that they are outcast? Merriam Webster defined outcast as someone who is not accepted by other people. Dictionary.com defined it as a person who is rejected or cast out, as from home or society. Wikipedia defined it as someone who is rejected or 'cast out', as from home or society, or in some way excluded, looked down upon, or ignored.
Hyoudo Issei can be called as outcast since the rest of the school perceived him as insect due to his perversion. Hachiman was also avoided and looked down upon due to his sarcastic behavior and dead fish eyes which makes people who converse with him feel uncomfortable. Hasegawa was avoided since they are scared of him as they think he is a yankee due to his blond hair which they think was dyed.
The rest was not avoided or looked down upon. There was nothing in the anime or light novel that suggests that they are a social outcast. Tigrevurmud Vorn was looked down but only by noble of higher status (greater political and military power) than him, Zion Thernadier. The rest, including Eleonora Viltaria, which boast greater military and political power, much like Zion Thernadier if not greater due to her status as a Vanadis, doesn't look down upon him. Adlet was looked down upon by only by some, due to his background. Most however, see him in good light since he is one of the chosen heroes.
So, out of 10, we have 3 pure outcast, that is 30%. While this is not a majority, it is quite a significant number. Why do we have this many social outcast protagonists? In Issei's case, he is a social outcast due to his open perversion, so his personality is the problem here. It is to be expected that he is a social outcast since he is so perverted. Hachiman and Hasegawa are the only ones looked down purely due to their looks. So it's really only 2 of 10 social outcast. Not that much considering the amount of samples.
Why do we have these social outcast protagonists? I think the main reason is that because having a social outcast protagonist helps in making the reader immersed in the story. Such protagonist invokes empathy from the reader, regardless of whether the reader was a social outcast himself or not, but is especially true if the reader was. An immersed reader will continue to read the story as they want to find out what happens, thus such protagonist helps making the book sells.
Of those 10, Orimura Ichika, Hyoudo Issei, Hachigaya Hachiman, Kirigaya Kazuto, and Sagara Yoshiharu are the ones with dark hairs. Dark as in black or dark brown. Tigrevurmud Vorn, Itsuka Shidou, and Adlet Mayer has light colored hair of red, blue and red respectively. Hasegawa Kodaka is in-between since his hair is actually blond but a dark blond. Tsuchimikado Harutora's hair is mainly light but he has black hair near his ears.
Of the 10 examples 5 has dark hair, that is 50% of the samples. Those who have dark hairs are all of Japanese ethnicity. Of those 5, Orimura Ichika, Hachigaya Hachiman, and Kirito are the ones with black hair. Hyoudo Issei and Sagara Yoshiharu's hair are dark brown. Dark brown hair is actually quite common among Asians.
Tigrevurmud Vorn, and Adlet Mayer was not Japanese. Japan doesn't even exist in their world. Itsuka Shidou, Tsuchimikado Harutora, and Hasegawa Kodaka are Japanese with light colored hair. In the case of Hasegawa Kodaka, his dark blond hair color is part of the plot. It was due to his father being a Japanese (with black hair) and his mother being a western with blond hair as he mentioned when he said that he is jealous of Kobato being born with pure blond hair and that she doesn't look like a Japanese unlike him. Shidou and Harutora has such hair color even when they were kids.
Blond however, is a color that people in real life also has. Shidou is the only Japanese with unnatural hair color. So, out of the 8, 7 has hair color that exists in real life. Only 2 has blond hair, which is not what most Japanese was born with. Thus, we can say that most of the protagonist with dark hair is because that is what most Japanese was born with.
Now, let's analysis how western media protagonists are. I'll just mention some.
Harry Potter of the Harry Potter series was a loner if we go by Merriam Websters' first definition of loner. He was also an outcast since befriending him means becoming enemy of the class bully, who happens to be his cousin, Dudley Dursley.
Bella Swan of Twilight series was also has friends prior to the start of the story, Angela Weber, and Jessica Stanley.
Batman is mostly a loner with his friend being Superman and that was after the story start, not prior to the story. He is also in friendly relationship with Robin, his sidekick.
Wolverine's friend before he joins the X-Men was his brother, Sabertooth. He is outcast as far the the humans is concerned since they fear him for being a mutant, that is if they found out about it.
Heathcliff of Wuthering Height was a loner and an outcast. He pretty much dislikes the company of others with the exception of Catherine who he is in love with. He is also an outcast due to his dark skin and origin.
I'm not saying that protagonist of western media are more loner and outcast than Japanese LN protagonists since clearly I didn't give enough examples. My point here is that this is not unique to Japanese LN protagonists. Such type of protagonist exists even in the 19th century when Wuthering Heights was published,
We can't really say that there is a trend of loner main protagonist in light novels. While we have quite a significant number of outcast main protagonists, it is not the majority. Like I said in the beginning, loner is not the same as social outcast. Only 10% of the example protagonists are loner, but 30%, that is 3 times, are social outcast. Social outcast protagonist invokes empathy from the reader which helps making them immersed in the story.
In comparison to other media, LN protagonists are actually not that unique. Loner & outcast protagonist is not exclusive to LN since like the example I give above, many protagonist of famous stories are loner and outcast.
In regards of hair color, it can be said that their dark hair color is due to the fact that most of Japanese was born with that, thus giving a dark hair color helps keeping it believable that the main character is a Japanese just like their name suggests.