No, I definitely use tmux for that stuff instead of whatever my terminal app has built-in - but usually I only have a single iTerm2 terminal open for my local tmux session, and any new windows or tabs are either meant for remoting into other servers, or are quickie one-offs that I explicitly don't want to connect to my "main" tmux session.

So when I hit CMD-T or CMD-N on my local machine, I don't _want_ to be connected to my tmux session, since I'd just have to hit `D every time to disconnect, and then run "ssh elsewhere" and connect to tmux there.