Terminal multiplexers are useful, but they should be integrated in the terminal emulator. Disclosure: I'm the author of DomTerm (https://domterm.org) which does that. Having a multiplexer emulate a terminal on top of a terminal emulator is wrong in multiple ways. Most obviously you're limited to the functionality that is common to both the multiplexer and the underlying terminal. The user interface is restricted: You can't re-arrange sub-windows with the mouse (drag). Menus aren't integrated. You have to use a special command-key that applications may not use. (With an integrated multiplexer you can use a command-key that applications can't use because it doesn't send an xterm escape sequence.) Different sub-windows can connect (and detach/re-attach) to different remote servers without explicitly running nested remote multiplexers etc.

I believe DomTerm can conceptually do everything that GNU screen or tmux can do, in a more integrated way. I say "conceptually": It has the major features but is missing some polish and minor features because it is less mature. (Help welcomed.) I'm current working on polishing "copy/view mode". The way DomTerm handles remote connections (http://domterm.org/Remoting-over-ssh.html) is mostly done and if-I-say-so-myself quite elegant and user-friendly.