> I'm wildly out of my depth here, but sometimes I find I learn quickly if I try out my intuition publicly and fail spectacularly :)

Fair enough. I believe this is a variation of Cunningham's Law, which states "the best way to get the right answer on the internet is not to ask a question; it's to post the wrong answer."

Everything you wrote about backtracking is completely correct. If I may paraphrase, it boils down to: cut can be used to avoid executing unnecessary code, but using it the wrong place will avoid executing necessary code, and that would be bad. My point is: the same could be said about the "break" keyword in C++: it can avoid unnecessary iterations in a loop, or it can exit a loop prematurely. Cut and break are both control structures which make sense in the context of their respective languages, but neither would be accurately described as "for optimization."