You can't stop people doing cover versions. Prince wanted compulsory license provision for songs removed from US statute.
What Palmer is doing is perfectly legal it just pisses all over his wishes hot on the heels of his death. He wouldn't be too thrilled about those other cover version either, if he were still alive they would have been pulled from YT. But none of those people got $35k to make them or are selling them online are they?
In fact just before he died Palmer wrote this, Amanda Palmer vs Prince, moaning that Prince got videos of her band covering all of Purple Rain in it's entirety pulled from YouTube:
http://blog.amandapalmer.net/20160315/
You've got to admire the hubris of equating her self to Prince ("I'm yin to his yang!") but this isn't a tribute, it's a tit for tat fuck you.
And this for charity? She got $35k to make that song and as with the Bowie covers (another $35k!) the charity donations aren't forever (she's explicit in saying all proceeds go to charity
for now). She's also using this in her tour which is ticketed. And if you want to claim her patreon money covers actual costs go and look for music industry responses to her breakdown of costs for the her kickstarter campaign.
To be honest I don't even mind all of that. It's the dissonance between her venality and presentation of herself as an artist when she's barely a step up from Mike Yarwood.