That's what RDP, VNC, etc. are for.

They are usually tied to specific user accounts, it's true. But that's something some people made up, and it doesn't have to be that way.

Well, it depends on what you want. I'm glad the Claude Code TUI runs in my terminal, for example, because that's where I do software development and interact with the file system and run other lightweight keyboard-driven TUIs that I want to use moment to moment.

Imagine if there were no terminal/pty system. Then what, I'd have to use Claude Desktop (doesn't support multiple windows) and Finder?

So no, it's not the only argument for TUIs.