Why is Bxh6 not preferred here? [FEN "rnb1k2r/ppppqppp/4p2n/4P3/2PP4/2PB1N2/P4PPP/R1BQK2R w KQkq - 3 9"]


I was just post-analyzing a game of mine with an engine and to my surprise in the position displayed above, it didn't even consider taking the knight on h6 as one of the top few moves.

Can someone explain me why that is? In many positions where the opponent's knight goes to a6 or h6 it's beneficial to take with an undeveloped bishop and I'm not sure why it's not here. It doubles my opponent's outer pawns which seems quite bad to me especially when he's likely to castle king side. Instead the engine prefers castling which allows the knight to go to f5 next square which seems like an OK square for the knight. 


Is my dark squared bishop that important in this position or what's the idea behind this?
Is my dark squared bishop that important in this position or what's
  the idea behind this?


Yes, your dark squared bishop is very important in this position. Your opponent doesn't have one, so yours is unopposed. Furthermore you have the minor advantages of the two bishops.

Doubling your opponent's pawns isn't as big a plus as you imagine in this position. Yes, it weakens Black's kingside but it also opens the g file for his rook which could, in the short term, more than compensate.

Finally, you have some very good threats with your bishop against the awkwardly placed Black queen. They don't quite work immediately but both Bg5 and Ba3 could be very embarrassing with the right preparation. A move like Qb3 prepares both and could be a good move to start with.