I don't mind "Partyman" and "Trust", I think they actually fit the Joker's character and in the context of the film. The Joker is ____ing insane. I mean, not only is he vandalizing and destroying art with his own twisted "artistic vision" he's dancing around innocent people that he just killed while he does it.
That's definitely the Joker. Do I like Prince? No, but everything from "Gentlemen, let's broaden our minds" to saving "Figure with Meat" because he "kinda likes that one" is great. I can't imagine the scene without it.
Trust, I actually like. It makes sense, "hubba, hubba, hubba, money, money, money, who do you trust". The Joker is like, the ultimate showman and once he notices Batman in the sky, the entire tone of the scene gets darker and changes when Trust dies down. It's appropriate.
The actual Elfman soundtrack is enough to counter and balance any problem I have with Prince being attached to the film. Nolan and other modern directors don't have that mandate to have record music deals with their films. Back in the 80s, it was practically essential. Batman, Terminator, you name it. I kind of miss it now but times are different. Everything is "serious business".
EDIT:
And Batdance isn't in the film. That wouldn't have made sense.