I do, when gaming.

I can think of some Portal puzzles in particular where timing is important, and you need to hold your aim but wait to click until something happens somewhere else on the screen (so the place you're clicking is not the same as the place you're looking).

I think the same thing applies to e.g. recording network activity in Chrome dev tools. My eyes are on the page to see when the thing I'm interested in finishes loading; my mouse cursor is on the button to stop recording.

It's not a super common pattern, but probably common enough that it would be annoying not to be able to do it.