Why is Bishop pins Knight so good?

Doing the g5 thing isn't really recommendable, since it weakens your kingside and makes it easier for your opponent to infiltrate it.

IceKane is exactly right. I just looked this up in a database, and below are Black's responses shown for his 5th move there, with the statistical outcomes. Note that with 5...g5 White's win rate soars to 83%, compared to only about 50-60% for the other move choices.

1. d4 d5

2. c4 {Queen's Gambit.} e6 {Queen's Gambit Declined, 'Bourdonnais Defense.'}

3. Nc3 {"Damaso Attack."} Nf6 {"Klovans Defense."}

4. Bg5 {"Alekhine Attack."} h6 {"Budde Defense."}

5. Bh4 {#1 pop. w 64%.}

5...Be7 {#1 pop. w 64%.}

5...Bb4 {#2 pop. w 53%.}

5...c6 {#3 pop. b 44%.}

5...g5 {#4 pop. w 83%.}

The OP asks a good question. As already said, it is because the king side is weakened. This is where black castles.

The OP should then investigate how white can make inroads against black in this type of structure. Hint: h4 might be useful at some stage with white's rook behind it. White might castle queen side.

That's why 4. ...Be7 is the natural response I think.

In some ways, one wonders why you bother with h6 if you are not going to bother to follow up with g5. (On the queen-side one often does follow-up).

I guess on h4 the bishop is more restricted than on g5, and the mere threat of g5 may prevent white taking certain actions like g3 to fianchetto the bishop. 

There are multiple advantages to ...h6, in any event:

(1) It creates Luft for the king, which comes in handy surprisingly often.

(2) If Black ever gets into big trouble with the pinning bishop, he can immediately free himself with ...g5 and incur only somewhat more risk, rather than losing in a major way elsewhere. If he waited to play ...h6, however, trouble could hit him so fast that there would be no time to first play ...h6.

(3) It forces White to make a choice of three common options (capture, back up but retain the pin, or retreat), and the more options a player has, the more likely they will go wrong, especially if they're a beginner.

(4) It's dangerous to have any of the opponent's pieces lingering in your vicinity, so this pushes the bishop to its own side of the board.

(5) It discourages later pieces to occupy g5 as well, such as a knight.

(6) True about the fianchetto mistake potential. I hadn't thought about that one until you mentioned it. That's yet another way a player can go wrong, and it happens a lot in beginners' games.

The Bishop is also much more exposed to tactics on h4 than it is on g5.

Here are two simple examples from my own games. In both cases, the Bishop would be perfectly safe if it was on g5 (g4 for a Black Bishop), but is exposed to nasty tactics on h4 (h5 for Black).

I think h6 is playable if White couldnt take on f6, Black would need to transpose into some sort of Nimzo which reminds me of Carlsen - Anand Leuven 2016 Blitz Round 3.

Smirnov did a little series about these. Many times he feels the pin is a bad move. https://www.youtube.com/watch?v=l_zWJHYWWJs Spoiler alert. He does like g5 a lot of time eventually when the Bishop will be out of play.

Ginger-Ash-Ville is good on the Queens Gambit. He recommends castling queen side for white when black has committed with h6.