I decided to ask Stockfish for some help for this one. After 9. d3 O-O 10. h3 black must either retreat (bd7 and black has allowed white to play h3 with tempo for free (which restricts the knight and bishop) or play bh5, keeping the pin.
Let's see what happens in a few moves:
1. e4 e5 2. Nf3 Nc6 3.Bb5 a6 4.Ba4 Nf6 5. O-O Be7 6. Re1 b5 7. Bb3 d6 8. c3 Bg4 9. d3 O-O 10. h3 Bh5 11. Nbd2 Na5 12. Bc2 c5 13. Nf1 Nc6 14. Ng3
and black must play Bg6 or Bxf3 otherwise white will get Nxh5 Nxh5 Nxe5 Nxe5 Qxh5 winning a pawn with a discovered attack on the knight. If black plays Bxf3 Qxf3, white will have the bishop pair and will basically inevitably get Nf5 (if black tries g6, Bg5 is very annoying. If black plays 14 ... Bg6 white will play Nh4 and actually doesn't even take the bishop: it is stronger to just play Nhf5. Also, if black tries any d5 stuff after Nh4, the idea is STILL Nf5; the dominant knight on f5 will force black to give up the bishop pair to keep white at bay in the endgame.
Even though this is just one variation really, the critical idea revolves around the Nd2-f1-g3 route, and if black tries to stop that stuff on the kingside there's always a4 for white. Even if none of this happens, you can argue that the bishop would be better somewhere else after the queen unpins with Nd2.
Hope this helps.