I also like this one since it illustrates how dangerous those innocuous little moves like h3 can really be, as this wouldn't be anywhere near as effective if the h pawn was not advanced.
Bxg2 doesn't actually threaten mate since the bishop is en prise. So black wins a pawn and white's position is terrible, but he can limp on for a while longer.
Pretty easy imo, Bh2+ Kf1 Bxg2+ Kxg2/Ke2 and Nf4+. Of course there might be a mate that I didn't bother to look for but winning the queen is good enough and I'm not going to bother looking for a mate.
Edi: Dire, do you really see h3 coming back to bite White because a heavy piece can't defend h2 from above? imo it's more often a problem when Black can get a diagonal piece on the a7-g1 diagonal and land a piece on g3.
There's no ABC reason why a move like h3 is not good. It's just a general weakening. This is just a position, like countless others, where it leads to a quick crush.