The sacrifice makes very little sense here. A weakness is only a weakness if it can be exploited, and in this case white won't really have anything substantial to go on after giving up the bishop. But why can I be so certain that white won't have any good follow-ups, even if I don't consider all possibilities? What aspects of the position make it clear to me that white will not be able to exploit black's "vulnerable" king?
If we look a bit more concretely at the position after Bxh6, gxh6, what do we find? We find an entire army of black pieces, all of them ready to leap into the defense of their king! In particular, the knight on f6 and the bishop on g6 are at least as good as a pair of pawns when it comes to shielding black's king from direct attacks, so it doesn't really matter that black's pawn cover isn't that great. Also worth noting is the rook on f8, which can be placed on f7, providing even more defense for black's king.
While it's good that you're aware of the fact that one always has to be careful with allowing this kind of sacrifice around one's own king, this needs to be tempered somewhat. Ask yourself questions like "how will my opponent follow up their sacrifice?", "can the opponent easily open up lines of attack against my king?", "do I have enough defenders around my king?" etc. and you will find it a lot easier to correctly judge whether a piece sacrifice with the goal of initiating a king assault is likely to succeed.