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.
Keyboard-driven GUIs belong in the realm of a lost art called "accessibility", which enabled people with motor issues (amongst many others) to use applications without a mouse.
FWIW, most of Windows XP's utilities and included software was perfectly usable with a keyboard alone.
And TUIs are only keyboard driven. So the choice for speed if you don't need graphics is always - TUI (or CLI).