Ah, but the question here is who's consuming the milk? It's the Pokemon itself that's consuming the milk, not the trainer. Now while this does take Nidoqueen out the the equation, this does still mean Kangaskhan can learn it as it'll the the child drinking the mother's milk (as for why the mother would regain HP for its child drinking its milk, either their HP bar is meant to be a shared HP thing or the drinking of the milk activates hormones in the mother that creates a healing sensation so it can produce more milk).
And I also thought about that latter point. Maybe there can be a Milk Drink move tutor for female Ponyta family (horse), Mareep family (sheep), Girafarig (it's sort of like a llama), Shuckle (stretching, but the berry juice it creates is essentially like fruit milk), Stantler (reindeer), Numel family (camel), Blitzle family (zebra are horses), Whimsicott (goat), Deerling family (maybe not a reindeer but close enough, right?), Bouffalant (similar enough to a yak/water buffalo), & Mudbray family (horse, and donkey).