Also, even though they may support a mouse, TUIs almost inevitably are very well keyboard driven, and typically do a better job of it than a GUI, particularly web GUIs.

It can be done with GUIs, of course. You can also have bad TUIs. But "out of the box", the TUI tends towards better keyboard navigability than GUIs, so are more likely to get something usable "for free".

I find it very easy to get "trapped" in GUIs where your keyboard falls in to a focus pit that it can't get out of.