Huh? To be fair, I don’t think you were setting out to make the case for deontology here. All I am saying about its “use” is that I don’t see any appeal. I think you gave a pretty good description of what deontologists are thinking; the North Pole—reindeer—haunting paragraph was handily illustrative.
Anyway, I think Kant may be to blame for employing arguments that consider “what would happen if others performed similar acts more frequently than they actually do”. People say similar things all the time—“What if everyone did that?”—as though there were a sort of magical causal linkage between one’s individual actions and the actions of the rest of the world.
That’s a very good point. But there may be a parallel counterpoint: “Sometimes parents are indulgent and too lazy or exhausted or undisciplined to enforce an appropriate degree of discipline in their own children. And the one relationship in the world that is probably most often characterized by unquestioning, adoring love is that from parents to their children. This is a reason for more than the usual amount of skepticism of arguments that say that liberal parenting is necessary.” Nothing makes most (… or at least many?) parents happier than making their children happy — so shouldn’t we expect a bias toward indulgence too?
Perhaps it would be better to weight our arguments about appropriate parenting styles based on the personalities of particular parents.