Why is g5 much better than gxh5 in this position of Anand?

Question

To me, Anand's 13. g5 instead of 13. gxh5 was very surprising.

[Title "Vishwanathan Anand vs Nafiz Ediz İlhan, chess24.com"] 

[FEN ""]

1. Nf3 Nf6 2. c4 g6 3. Nc3 Bg7 4. e4 d6 5. d4 O-O 6. h3 e5 7. d5 a5 8. g4 Nfd7 9. Be3 Na6 10. Rg1 Ndc5 11. h4 Kh8 12. h5 gxh5 13. g5 Bg4 14. Rxg4 hxg4 15. Nh4 Qd7 16. Be2 g3 17. Bg4 Qe7 18. Bf5 gxf2+ 19. Kxf2 f6 20. Qh5 Bh6 21. Qxh6 Nd3+ 22. Ke2 fxg5 23. Ng6+ 1-0

My reasons are:

1. With rook on g1, 13. gxh5 gives it a direct open file against the king.
2. 13. g5 allowed 13... Bg4, necessitating 14. Rxg4, an exchange sacrifice for the attack to continue.
3. The fundamental idea of any pawn storm, such as that attempted by Anand, is to exchange pawns in front of the king.

It is clear that Anand considers gxh5, but finds it so bad that he says "I might have been a bit careless here"!

This completely took me by surprise.

Why is 13. gxh5 so bad? And 13. g5 much better?

Answer 1

1. With rook on g1, 13. gxh5 gives it a direct open file against the king.

Wrong! The black king is not on the g file. It is on the h file and the rook on f8 is ready, if required, to come to g8 and fight for the open file.

2. 13. g5 allowed 13... Bg4, necessitating 14. Rxg4, an exchange sacrifice for the attack to continue.

Again, wrong. 13... Bg5 14 Rxg4 hxg4 really does open the file the black king is on, the h file. "allowed" is wrong and so is "necessitating". This sequence accelerates the attack. Without using an engine, 13... f5 looks to be better for black than Bg5, or at least less bad.

3. The fundamental idea of any pawn storm, such as that attempted by Anand, is to exchange pawns in front of the king.

Which is what happened in the game (white got rid of his h pawn, opening up the h file against the black king, and got rid of the black g pawn which was defending h5) with the bonus that white's g pawn was retained as a threat.

Why is 13. gxh5 so bad?

It blocks the h file (the file the black king is on) with a white pawn which white can't remove.