The best UIs IMO tend to be those that allow operation with the left hand on the keyboard home row, and the right hand on the mouse. Keyboard shortcuts should be preferentially towards the left side of the keyboard. Quite a bit of CAD & graphics software works this way.
Keyboard-only is decent for text, and particularly good for text where everything that needs to be edited will be on the screen at the same time.
I switched to using the mouse with my left hand because of this. One day in the middle of a long coding session I noticed I was moving my right hand back and forth a lot between the keyboard and the mouse, so I picked up the mouse, moved it to the other side of the keyboard, and started using it that way (still in right-hand configuration). I've been using it that way for over 30 years now.
Because I kept the mouse in right-hand configuration, I can use any mouse with my left hand without having to switch the buttons, and I can also still use the mouse right-handed.
I call this model the "MOBA interaction model", because in those games (which include League, Smite, and Dota) you must place do exactly this.
I, too, wish that more interfaces worked this way - but there's a fundamental problem, which is that many tools (including all Unix ones) are more efficient when you can input text, which necessitates the use of both hands on the keyboard.
Not quite the case, thankfully. I'm left handed and greatly benefit from this style of keyboard layout. I tend to notice that I'm more finger-agile with my left hand, which helps with quickly chained left hand shortcuts (C-z/x/c/v/a/s/tab, M-x, anything with shift or windows) and WASD movement.
As for the right, as some other commenters have noted it really isn't that bad to use your non-dominant hand with a mouse. Most of the movement precision comes from the wrist and elbow, rather than finer finger control.
Keyboard-only is decent for text, and particularly good for text where everything that needs to be edited will be on the screen at the same time.