I played this game in the Alekhine's Defense: Four Pawns Attack and I was crushed as white. I could not find a white improvement to this game which worries me on the viability of the Four Pawns Variation.
After review, it appears that I could have played Qh4 instead of Bxh6 for a worse endgame, but survivable. I did not play this opening to be barely survivable!
Alekhine's defense is a duffer's defense. A grandmaster played this defense against me and I got a clear advantage into the middlegame, where, by virtue of his skill, he crushed me.
But the defense is easy enough to face. Getting an edge is easy:
e4 Nf6 e5 Nd5 Nc3! Nxc3 dxc3 Nc6 f4!
From here, you have a wide open, but safe center. Your doubled pawns help paralyze the enemy knight, and you have a great space advantage to the kingside. Develop your pieces and castle queenside.
There are a lot of lines that lead to an advantage for white in the Alekhine's Defence. But what I am concerned about is the four pawns.
I mean that is like saying the way to avoid the Ruy Lopez is the Petrov. While that is true, that is not necessarily relevant.
As an ex Alekhine player i have some suggestions.
First, regarding the alekhine in general: it's not true that there are tons of lines laeding to W advantage. The modern (1.e4 Nf6 2.e5 Nd5 3.d4 d6 4.Nf3!) is probably the only line where W can claim a theoretical += with best play (probably the solid Miles variation ,...dxe5 5.Nxe5 c6, is B best). The exchange and the 4 pawn attach should be ok for a prepared black. The Chase variation is at best = for W. Early Nc3 lines are a way to play an equal chess game, not to claim an advantage. The Aleknine has always scored reasonably well and has been used succesfully in WC games (with B scoring 1 win and 3 draws). So why it's so rare?
I think the real problem with the Aleknine is the freedom it concedes to W. I mean, W is a fierce tactician? He goes for the 4PA. W is a solid player? The exchange or the modern will suit his style. When B plays 1...Nf6, he has no idea about which sort of game is coming. This is a serious problem for a GM, who sometimes needs a draw and sometimes is out for a win. I think this is the best explanation for the Aleknine being less popular at GM level than, say, the Scandinavian.
Bach to concrete variations: The line metallictaste suggests is a common anti-alekhine, leading to an = but interesting game. 4...Nc6?! in your line is a mistake.
B has 2 options:
-The solid 4...d6, often leading to an early endgame. 5.Nf3 dxe5 6.Qxd8+ Kxd8 7. Nxe5 Ke8. A lot of GM have defended easily this endgame as B, but it's not a very exciting way to play.
-4...d5! is more fighting. As you say W plans a quick 0-0-0 a kingside attack. Howewer B is not without his own play. He will advance his queenside pawns (this is why Nc6 is not the move, blocking the c pawn) and organize a tremendous counterattack. Give a look at the often quoted game Adams-Agdestein Oslo 1994 (1-0) W won the game but was close to lost before the opponent blundered(17...Be7?, better Qb6 or b3. Also could have improved earlyer with 13...Be4), and already worse out of the opening. Both sides have improvements of course.
Bach to the original question: i used to score very well against the 4PA as B (around 80%). It's not a bad weapon at all if W knows the theory, pity is that there is a lot of theory! I don't think it's a sensible choice for a non-professional.
In your game both sides followed the main line until 19.Be2.
Unfortunately i used to play a different line against the 4PA and i'm not at all an expert in this line. I have added some deviations for W, i will come back later if i manage to find something in the game line.