I don't think there's anything wrong with being bad at singing as long as you readily admit that you are a novice.

I did a lot of community theatre when I was young and there were plenty of people who were firmly in the camp it sounds like you're describing. Really bad, trying to emulate the style of pop or stage performers but not understanding the technique.

They think they sound close enough and to the untrained ear, they do so they get a decent amoun of praise which makes them dismiss any notes from people who actually know what they're talking about- people like their music directors etc

This is true very generally I would say, like you have to do a lot more digging but there are games that deviate from this chibi style you're referring to. Blazblue or any of the SMT games come to mind as examples