For sorting, conveniently we always definitely need to look at all the elements at least once anyway, so although even the early introspective sorts from the end of last century aren't designed this way both the Timsort and a modern sort like a PDQ sort will end up making that decision early.

"Oh, this was mostly already sorted, done"

If you meant exactly rather than almost then you can still squeak a small win from having an algorithm which is optimised for this case but the vast bulk of your runtime is eaten by the unavoidable work of checking. "Don't check" is faster but then you're not a sort algorithm at all.