A GUI can be keyboard-driven and as fast as a TUI. The sad truth is that the status quo for GUIs is absolutely terrible, and most were rushed out and not properly tested to check if they're really usable without a mouse.
This is the key point. No platform UI paradigm focuses on keyboard navigability and speed, all focus on mouse and visual effects for discoverability in a pursuit to dumb down the user experience enough to make it usable for everyone, breaking power users in the process (and increasingly also accessibility stacks).
And TUIs are only keyboard driven. So the choice for speed if you don't need graphics is always - TUI (or CLI).
Plenty of TUIs support mouse to various extents too. Claude Code is an obvious example (try the scroll wheel for example).
I agree with you that TUIs are keyboard driven first though - and so you can be certain it will work well.
Not so. GUIs absolutely should be keyboard-drivable, if they're written to the human interface specs of whichever platform they're hosted on. That doesn't mean they don't support being mouse-driven or even that mouse isn't the default, but in my experience if the developer has taken any sort of care with the interface then keyboard interaction will be at least as good, if not better, with the keyboard.
> And TUIs are only keyboard driven.
Not true either. There's a line in my .vimrc saying "set mouse-=a" specifically because I want to turn off the mouse in that particular TUI app. If a TUI app doesn't support the mouse they've just not added that support, it's not that it's not possible.
Absolutely not.
The problem is discoverability. You need to go out of your way to learn shortcuts.
FWIW, most of Windows XP's utilities and included software was perfectly usable with a keyboard alone.