"I don't get the draw of "When Doves Cry" at all"
Yeah I'm generally not a Prince fan and have always been baffled by that song's popularity in particular- somewhat catchy melody but also awkward like you say and the lyrics are pretty cringe-inducing too. I also feel like "Purple Rain" gets pretty overrated in general- I get that it was a big event especially when coupled with the movie but none of the songs are among Prince's best (interesting that Trung considers the title track to be Prince's best song- yeah it's melodic but the melody is generic wannabe anthemic campfire singalong type bullshit).
"Kiss" is my favorite Prince song but as you say it's largely due to the groove but I also love his falsetto (wonder why Trung didn't pick up on that given his love of falsetto singing in general- arguably one of Prince's greatest strengths). My other favorite Prince song is "Raspberry Beret" which is arguably his strongest melody. And yeah, Sinead's "Nothing Compares" is great and better than Prince's version (IIRC the version I've head is just him singing it live at the piano).