I've been trying to figure out what the fuss is about, and I still really don't understand (apart from persistence and screen sharing.)
When I want multiple terminals, I just fire up another terminal window and hey presto, jobs a goodun. I have a fairly high res screen and small fonts, so I can fit many terminals on one screen. If I run out, I hop over to a new virtual screen.
Perhaps this is a by product of working in linux/unix so long? I can imagine that if I was forced to use putty, where connection setup is costly and screen space scarce, I'd want tmux to make things quicker.
What am I missing?