Well as I have said the reason not to play it is to avoid the 7 Bxf6 lines. It's not nearly as common as 7 Bh4 but it's still a good option for white and one I don't feel like preparing for. Maybe that's lazy, but I have a tournament coming up, so I don't think in the short term it's worth it just to get such a miniscule "improvement" if it even exists in the lines I'm playing.
Oh you're saying 5...h6 (not 6...h6) is the modern move (which I don't think is true; 5...0-0 is definitely most popular, but after 6 e3 h6 is overwhelmingly popular [as a matter of fact, 6...b6 is a very rare move!]). I don't think the plan shown by white is supposed to be overly critical though; it's reasonable but black's bishops should have enough targets to balance the game out, and I don't even feel I would need to prepare for it too much if I was playing a long game.
So playing ...h6 and not playing ...h6 seems to offer different extra options for white in either case: ...h6 allows Bxf6 with no loss of tempo, not playing ...h6 allows the Qc2 plan. Thanks for posting that example.
. I suppose they figure if it's good on move 6, and castling isn't urgent, then why not on move 5.
So apparently 6...h6 is the "modern" move before going into a lasker or tartakower defense, and I was well aware of this for a long time. I can understand the benefits of this move if you want to play a lasker defense, but personally, I think it has extremely minimal to no benefit in a tartakower defense, because the defense of h7 shouldn't be an issue in this type of position where white's best idea is to play positionally, on the queenside or center.
The main drawback to playing 6...h6 is that white can play 7 Bxf6, which has its bite, but if black had played 6...b6, 7 Bxf6 would probably just transpose into normal tartakower lines but without ...h6, which I think is no issue whatsoever.