The problem with this is using tmux screws with using mouse for selection (since tmux takes over the mouse and does its own selection thing, which usually doesn't do what I want).
This approach also means you can't do anything interesting like what Terminal.app does with detecting prompts, marking them, and letting you jump back to them (or clear history back to them).
This approach could be excused if the terminal actually natively integrated with tmux, thus providing its own gui splits/tabs that represent tmux's panes/windows, but it doesn't sound like it does that.
