all the examples for visual UI, are tasks which already are (or soon be) done by the agent, not human. hence not needed.

I suspect that final(*) UI is much more similar to TUI: being kind of conversational (human <> AI). Current GUIs provided by your bank/etc are much less effective/useful for us, comparing to conversation way: 'show/do me sth which I just need'. Not to mention (lack of) walled garden effect, and attention grabbing not in the user interest (popups, self-promo, nagging). Also if taking into account age factor. Also that we do not have to learn, yet another GUI (teach a new bank to your mom ;). So at least 4 distinct and important advantages for TUI.

My bet: TUI/conversation win (*).

*) there will be some UI where graphical information density is important (air controller?) especially in time critical environments. yet even there I suspect it's more like conversation with dynamic image/report/graph generated on the go. Not the UI per se.