I feel like the answer to this question is always, do the best you can to find the illusive happy medium, because both staff-run plots and the feeling that I can do shit if I want to do shit are necessary for me to invest in a game. What turns me off are the extremes. I'll leave a game where staff runs no story much faster, I guess, because I'm just not into the disconnected sandbox 'All PrP all the time' thing. It's just not a style I particularly jive with.
I prefer scheduled scenes these days because otherwise I'm, realistically, going to miss most shit that happens, just because my time is somewhat limited and MU*ing is a thing I fit in (and I'm not nearly as limited as a lot of other players, even with that). Doesn't mean I h8 the idea of impromptu scenes, just that I'm probably not going to be able to get in on stuff if all scenes are totally rando. I also think STs should have the freedom to do unpredictable shit if they want, though. Like the above, I think it's a balance.
I've also, honestly, never thought of 'PrP' as 'do something vaguely more interesting than meet-and-greet coffee shop RP'. I think of them as actual plots, however long they last, that are a bit more involved than random one-off scenes you decide to do off the cuff one night. I come from cultures where if I want to run a random bar fight, or do little riffs with an NPC in the background of a scene, that's just regular RP and I've never had anybody get weird about it with me. I get that this isn't the case everywhere, though, and this is one of those conversations that seems to come down to 'how are we defining this word' as much as what people want out of PrPs and game rules surrounding them.