TUIs are as cross-platform and network-able on as many clients as you are able to run SSH clients on. They also support resuming (via a terminal multiplexer such as Tmux/Screen; tmux itself can also support session resuming via a plugin), windowing/tabs (via term mux), scrolling (via term mux). So your TUI program does not need any of these features. If you have a computer running 24/7 you can connect to term mux over SSH from anywhere you want. If you have high latency such as LTE or bad WLAN, you can use Mosh to easy with the latency. Either you, you aren't using a lot of bandwidth with a TUI. You can also use the power of the UNIX shell easily together with a term mux. For example, jessfraz runs all her CLI commands in Docker.
Why I like it? Well, if you're a Emacs user and you can get everything to work with Emacs-esque keybinds that's great. Same with vi(m) keybinds. With Mutt, its a matter of setting EDITOR right and you can compose your e-mails with vi(m) (yes, you could set EDITOR to something more nefarious ;). You don't get to make such choices with a GUI e-mail client.
Why I like it? Well, if you're a Emacs user and you can get everything to work with Emacs-esque keybinds that's great. Same with vi(m) keybinds. With Mutt, its a matter of setting EDITOR right and you can compose your e-mails with vi(m) (yes, you could set EDITOR to something more nefarious ;). You don't get to make such choices with a GUI e-mail client.