I'm A Banana
Potassium-Rich
It's not roleplaying to roll your "Perform (Exotic Dance)" skill. It is role-playing to decide to use it, to describe what your character wants to dance. That is the "real" roleplaying part.
Why d'you say that?
See, playing a role is what it means to put your mind in the frame of another being and act as if that being were to act.
In a role-playing game, your actions in that role require you to play a game to resolve in the world. A game using rules.
In D&D, this means rolling dice.
Rolling for a Perform (Exotic Dance) skill or for a Morality check, or taking damage because of an alignment...
All of these are the very essence of a Role Playing Game.
Without the game, without the dice roles or the rules, you're just role-playing. Which is fun, but definitely not what I'm playing D&D for.
Does it become more role-playing if you can dance an exotic dance and use your "per dance" power "Stunning Jump" that causes the audience to take 1d6+CHA points of impression damage?
Sure. It means that the role that you play affects the world by giving the spectators an impression. If that impression damage makes them more likely to, I duno, give you money, then the game models playing the role of a dancer who persuades his audience to tip him. This makes sense in the context of the role of a performer, so it helps you play your role better.
I agree that such skills should exist in a game, and that the rules should work for it. But it makes little sense in making the rules more complex for them and pretending that means you have more role-playing now. You have just using people using a different part of your game system more. (I'd say it's okay to want making the rules for them more complex - if that makes the game mechanically more interesting. But I'd say that from all mechanical systems, combat systems are probably the most useful for a game that is played with multiple players that want to share the mechanical game experience)
The idea that mechanics aren't role-playing (and vice-versa) is a wildly inaccurate and false idea. In a role-playing game, mechanics are the only way you truly play your role in both senses of the word (that you are playing a game and playing a role at the same time).