Well, in The King of Fighters' defense and I guess, Street Fighter, both have two main characters instead of one. Ryu is, yes, a stoic, old-school warrior, but granted, he was created in 1987 which I guess was a time when stoic warriors were popular in Japan. Nowadays, we have the stupid, invincible, oblivious, power of friendship, I'll never give up, I'll overreact, I have a childhood love interest, catchphrase or signature attack heroes - man, I wish we had more Dantes, more Alucards, more other, interesting characters. Anyway, I digress. So, in Ryu's defense, he's an old man compared to the new age of colorful main characters like Sol Badguy, Ragna, etc. Hell, I think it's said that Ryu is kind of backwards or more conservative.
To counter this, we have Ken Masters, who like Ryu was created in 1987. I guess, he was created based on what people thought of Americans, but I think a little of Karate Kid (1984) influenced some of his character. Ken is more vibrant; he's loud and expressive in contrast to the type of heroes popular in Japan, but popular in the United States, however, Ken is also respectful when it comes to where he learned martial arts. Likewise, I think Daniel LaRusso was like this, he started off as a reckless, impatient boy who wanted to learn karate mostly for means of being strong, but as time passes, he learns that karate is more of an art and something to protect people instead of for glory and power. Ken is more exaggerated since Street Fighter is more fun than moral story, still he has similarities to Daniel.
For KoF, Kyo Kusanagi was created in 1994 and he's based on the juvenile delinquent hero that I assume was popular in Japan in the 90's. As I type this, yep, YuYu Hakusho started on December 1990 and guess what Yusuke Urameshi is? A juvenile delinquent hero. The difference is that Yusuke is more expressive, lively, and fun while also creating a strong moral compass as the story goes on. Kyo is simply put: a jackass. He's proud of his heritage, does not seem to give a damn about anything except fighting, and he's really arrogant. I don't think he grows in character beyond that, he just remains as an immature character. That said, he embodies the juvenile delinquent in a bad way, one who does not grow like Yusuke or Tomoya Okazaki from Clannad. Kyo always tries to act like a badass but it usually makes him look like an ass more than anything even though he's supposedly well-meaning with a strong sense of justice.
The other "hero" or anti-hero, would be Iori Yagami. Personally, I think Iori is much more interesting than Kyo. Even though he's stoic, he's much more brutal and twisted; he might even be mentally or emotionally unstable. Because of his clan's curse, the Yagami hate the Kusanagi; the Yagami then known as the Yasakani made a pact with Orochi for power. That power usually makes them really aggressive especially against the Kusanagi who they were jealous of in the past and caused them to make the pact. Also, as part of the curse, the mothers will always die in childbirth. So, that leaves Iori without a mother and his father dead. Iori instinctively hates Kyo because of their clan's past. Iori murders people, usually by accident, in his rages despite him saying he dislike violence and will work with evil people just to get a chance to kill Kyo even if that means the end of the world. At a certain point, he loses his powers and loses his clan's curse. When he was given the choice to receive his powers and therefore be cursed again, he took it. I think Iori cares more about killing Kyo than anything even if that means making a deal with the devil and damning his entire bloodline. Also, it's said that there's another voice inside him that taunts and belittles him. It gets to the point where Iori questions if that's the real Iori, the bloodthirsty, twisted voice inside of his head and not the antisocial, loner Iori who claims to hate violence. So, we have a sick, twisted, though stoic at times character to contrast the stoic juvenile delinquent.
Anyway, the other SNK characters are much more colorful minus some of them like K' who is like Kyo, well, like Shadow is to Sonic. The characters tend to go from one side to another like a KoF character would be in Fatal Fury and vice versa. Fatal Fury stars Terry Bogard who is basically a 90's American stereotype with a vagabond life style. So, a parody of Musashi Miyamoto perhaps? As a character, he's kind of like Kenshin Himura but more casual and playful. Rarely does he ever get serious and dark and that only happens to Geese Howard who killed his father.
Long story short, I think the issue with fighting game personalities is that most fighting games come from the east and were created long before fighting games like Skullgirls and Blazblue, along with playing with stereotypes and trends at the time unlike Guilty Gear which was released in 1998 or Mortal Kombat which was released in 1992 and basically took every trend, stereotype, martial artist movie fans' fantasy and made a weird, funky, bloody creation of pure what the hell that took the world by surprise and spawned the ESRB due to fears of creating psychopaths and deviants in society. Still, MK has stoic characters, actually, most of the cast are stoic, but they have crazy ones that stand out. And generally, fighting games are just about the gameplay, hell, if they wanted they could make a fighting game with the characters - if you could call them characters - who just grunt and do victory poses when winning, have no backstory, personality, names, distinguishing features, or even faces and people are bound to play the game if the combat was amazing. No a ton of people, but enough that it would be a niche title or cult classic.