Ironically though, I’d argue what Prince did here was not fair use.
Unfortunately, that's a bad example, since Weird Al always gets permission from the original artists/songwriters/composers as may be the case. For example, he scrapped parodies based on Lady Gaga's songs because she (or the record company?) denied his use, although it's available online (non-commercial distribution): https://alyankovic.wordpress.com/the-gaga-saga/. Will he pass the four factors? He thinks so, but he still thinks it's a bit rude to not ask for permission.
Strictly speaking, Prince featuring an image of Dave Chapelle in parody of him on the cover of a single is neither hypocrisy nor idiocy. It is fundamentally one of many examples of self-parody, which is common among artists. While judgement as idiocy is highly subjective, Prince obviously put thought into what is far more accurately described as clever, but I don't see how it could in any way be hypocritical.