With me, I don't think I purposefully do it as much as I tend to fall into it. I always make a character that fits the setting, which includes their appearance. I tend to play in a colorful fantasy setting more often than not where it seems NOBODY has imperfections, but I'd very much play someone a bit uglier if the setting called for it. Stuff like my current RP, Duel Academy,  is based off of a few related shows that only have a handful of 'imperfect' characters among them. Even then, they're not so imperfect since they fit their designs well. The other RP I'm in, EoD, is a sort of 'Crushing idealism' thing. We all play an ideal of SOMETHING, whether we realize it or not, only to eventually have that character be broken by the setting.

So in the two above examples, I play idealistic and 'attractive' looking people. There were two RP I joined here that fit a less idealistic character, and I took that chance. I don't remember the first one's name and it never really took off either, but I made a 40 year old veteran that had his age showing in there. The second was something to do with a bunch of 'adventurers' out for fame and glory, but in a murky world. I think it was called 'Rask's horn band' or something along those lines. The nicest one among them was a snob and while looking pretty, was also realistic. My character was another adult that had quite an unattractive personality and imperfect features. Stuff like that is where I play my less 'attractive' characters.

So you could say I fit the setting, but I tend to gravitate more towards attractiveness and idealism because that's just the kind of settings I end up playing in more often than not.