Hmmm... I would find this extremely error-prone. Probably due to my own issues, but flipping through multiple remote sessions in tmux in the same window would get confusing after N=2 terminals.
But who manages THAT many remote sessions? Seems like an upstream problem to me, no?
I always want to emulate my seemingly-more-efficient colleagues. One of them had a set of 6 sessions in some layer talking to screen which was talking to vim or XXsh (bash, zsh, or something), and he had memorized an arrangement whereby he could think "I'm in this one and I want that one" and he'd go left-left or right-up and be in the right one. But he always had one unused when I would visit him and would pursue a search in that one. None of this was remote by the way. This inspiration got me to try screen but I didn't like it after all. It in no way inspired me to run Vim because I already preferred Emacs.
But who manages THAT many remote sessions? Seems like an upstream problem to me, no?