Whereas I use it primarily for the persistence layer, since I'm often sshing on a flaky connection and it's nice to be able to leave things open and be able to come back to them, or to attach to a session I left open on my desktop when I'm away.

Tabbing/windowing is a nice bonus; I don't use tiling in tmux all that much, since as you said, it can be done on a different layer, but it is occasionally useful.

My biggest frustration is that there are like ten million places where you need to tweak options to have it behave like a normal shell (scrolling, selection, etc.). It would be nice if these were less quirky by default.