Okay but TUIs don't matter here though right? You can easily run GUIs over the web with any box anyway if you wanted to. So how is your headless sever running 24x7 (which is what allows feature you talk about, not tmux or tuis) not the reason you can do that but TUIs are?

I have a windows box that never shuts down and i remote into it and use it GUI mode to do everything you said but with a proper GUI interface. I also use the terminal but your feature (constantly up + resume + multi device) does not need TUIs to even work.