That's also the reason why I prefer symmetric character designs in fighting games. Originally it was to cut costs (drawing and data storage), but it also makes learning anticipation easier and that's why some of the polygonal games also do it (e. g. Street Fighter IV).
Skins can also be bad in shooters because of adding all sorts of noise to the actual collision geometry and different colors have different advantages. In Quake III all characters have the same simple collision box, but very different shapes (there is an eyething with legs that is rather small). Quake III also had the solution though: you can just set on your side to see the same model on everyone.
All fighting games should offer the same option. At least the online mode should allow the individual player to always see the default costume (winning screens excepted). For offline matches you need a house rule for default costumes. (It could also be directly integrated into the interface of the fighter select screen that the other player has to approve you choosing an alternative costume, but I think that would be kinda autistic. Just talk to the other person ffs.)