There are other client/server solutions than VT100 terminals. X11 being one of them. And you can run a remote Emacs server and connect to it via emacsclient without being constrained by several emulators as middlemen.
Plan 9's sam had a similar client/server switch, mostly because the programmers didn't really like a) character graphics and b) their host systems.
That's a good point. I've never written a client that is "multi-interface re-entrant" like that (I have used and enjoyed emacs-client). The nice thing about character cell terminals is that all the terminal handling falls out for free: I don't need to accommodate for anything (like tmux, or remote access (like ssh)), it Just Happens.
Worth considering (or modeling) how I'd write an emacs-client type of application though.
Plan 9's sam had a similar client/server switch, mostly because the programmers didn't really like a) character graphics and b) their host systems.