I believe part of the reason is some identification people have with some characters. For instance, some army guys would love Guile, and it is a fact that most girls would play Chun Li. Ask the average 30 year old who Chun Li is: she knows her as much as she knows Mario. It is also the reason kids today love Ben 10. Ever been to a male kid’s birthday party? Half of them around here have Ben 10 stuff.
I personally dislike Anime cos it lacks the character traditional drawing gives to characters. While there are exceptions, the default is some template people fill with different eye and hair color, and “hair” form (or whatever they have in their heads). I loved anime when I was a kid (Zillion, mostly, I found Dragon Ball too slow or something), but I just favored traditional style cartoons and comics more. I learned to admire masters such as Barry Windsor-Smith, John Buscema, Jack Kirby, Alfredo Alcala, Joe Kubert, and Galep and several Italian artists. I particularly like B&W drawings as they can often portrait more details than classic color comics could. I believe the comparison with the in-game art of vanilla Super Turbo and the redrawn graphics in anime style and HD are a good example: despite having better resolution, the new graphics are arguably worse and less detailed, due to using less colors and less facial and muscle traces.
While there are quite old anime games, like the alpha series, several of them have been released those years Capcom stopped releasing good fighting games and SNK became SNK-Playmore. Games by then had to compete with MvC2 and CvS2, which had a big roster and - specially MvC2 - lots and lots of long and flashy combos. They went this route, for flashy stuff and long combos. I am a fan of classic SF2: positions, counters, zoning, hard to obtain positions and hard to escape when you allow your enemy to get a good position, that sort of stuff. Combos were, mostly, not a factor, since 3 or 4 hits and most characters felt dizzy, already. Many matches would not have combos: just simple attacks, throws and chip damage. Simply being able to jump over projectiles an inch closer than your opponent gave you a big advantage: anime games and Marvel give characters several ways of dealing with projectiles, including air blocking.
For me, that’s it. I’m relatively old, and still miss the magic SF2 brought. In some places, arcades are still alive, and it is cos of no other reason than SF2. It’s why SRK and GGPO even exist, and the only reason I still play games.
Edit: this is a good example of Barry Smith’s art. Nowadays, one would get a template with those leaves and repeat them over and over. Barry drew every single one of them. In addition to it, he managed to, somehow, imagine how the leaves and the character would look like if some sort of fence was between the scene and the imaginary light source. It goes unnoticed the first time you see it, but it is absolutely brilliant.