Supervillains bother me. Not in the same way they bother someone like Daredevil mind you. The idea behind supervillains bothers me. Why would someone create a new identity in order to commit crimes?
If a person wants to remain anonymous, they hide their face. This is the basic concept behind the costumed persona. True, some people wear a mask to adopt a better identity (e.g. Bruce Wayne is a man, but Batman is something more), but most characters are disguising themselves. Following this train of thought one would assume that the supervillain wears a disguise to keep themselves out of jail. If this were the case then they would wear traditional ski masks or ladies' stockings. Supervillains choose to wear disguises that are distinct and recognizable. Why? Because they want to get credit for what they've done but not get caught. They could easily rob banks without using insignias or gimmicks, but they want to be noticed.
I know that not all supervillains fit this mold. Eric Lensherr isn't dressing up and calling himself Magneto in order to avoid getting into trouble. He does this in order to separate himself from the likes of us humans. Nor does this apply to Killer Croc, who actually sees himself as a crocodile. The prior statement refers to the those such as The Wrecker, Captain Cold, Bullseye, and KGBeast.
The original Red Hood had the right idea. A criminal organization would pick a guy at random to put on this suit and lead the gang for one job. This protected the identities of those involved as well as help maintain the belief that there's one guy running the show.