So would a Buddha try to help people reflexively, without caring about whether he or she succeeds? That would be a recipe for half-assed compassion at best, no?

And why would the Buddha have selfless rather than selfish impulses? We try to catch a bus for self-interested reasons, yet a Buddha could have no such motives. So the mystery is what an enlightened person would try to do, given that such a person couldn't really want anything.