I'd rather have the window manager manage all those persistent shell sessions. But tmux is such a beast that most people use is as their window manager in a window manager as well. It's a bit kafkaesque to run a seperate tmux for each shell you open, but those other detach alternatives don't seem to work as reliable as tmux.
I have a weird annoying mix here: I also use tmux with multiple windows inside, but e.g. my irc client is in a single screen session