Prince is actually a very funny person in real life. There's some great outtakes of him clowning around, doing voices, cracking jokes. I even have a recording of him and the Revolution playing an OTT, sped up, heavy version of "When Doves Cry", in a punk style called "When Doves Scream", they were doing it for fun.
I'm just saying, it's not like he's some super serious person which it seems like he is by not allowing Weird Al to do a parody. Maybe he legitimately just doesn't find Weird Al particularly funny.