What benefit would you get if tmux itself became a control mode client?
You'd get pretty much same experience, with textual splits, modeful keyboard shortcuts to access scrollback & copy/paste etc. — which I'm not saying is bad but tmux already does that. Well, I suppose over ssh it'd allow you to access remote tmux session(s) from a local tmux, so maybe allowing little more flexibility mixing panes from multiple remote hosts(?) But still pretty much similar.
The whole point of control protocol was to allow native [G]UI where each pane feels like a native standalone terminal, no?
1. Ability to use local tmux configuration for tmux sessions over ssh. So I don't have to worry about using the default bindings when connecting to a host that doesn't have my tmux config, mouse support is already enabled, etc.
2. Ability to combine and organize remote panes alongside local panes, or panes from other remotes
3. Avoid ending up with nested tmux, where I have a remote tmux session inside of a pane of a local tmux session, which is a pretty terrible experience.
I'd also love it if linux terminals supported it too, but that doesn't seem terribly likely to happen anytime soon.
I looked into this at one point. IIRC it turns out control mode was only added to tmux by the iterm2 dev, for use in his own project. So I guess he didn't care about adding support to tmux itself.
It is pretty annoying that the only terminal that I know of that supports tmux control mode only works on mac.