I’ve never done it myself, but I’ve seen it done a few times on another site. I think the organization of the other site makes it more conducive to finding a new partner for a dead thread; here you’d first have to draw someone in to your interest check, then hope they have an interest in your proposal, whereas everything is a little more centralized over there. It was by no means common, and people wanting to restart a thread was definitely more common than a thread actually ending up restarted (probably most for the reasons BrokenPromise mentioned).

I personally don’t see an issue with it. I can see why people might find it invasive or distasteful, but I don’t see it as any different than playing canon characters from a fandom you like- it’s not for everyone, but there are people out there who would be down.

If you were to share an RP run in a [i]PM[/i] thread, I would find that a little more iffy, because to me private messages do come with some expectation of, well, privacy.