1 e4 e5 2 g4?

Interestingly, although the king's indian attack is not a bad line against some black defences and there are other decent lines with e4 and g3, the eccentric 1. e4 e5 2. g3?! is inferior (if far less so than 2. g4??). The reason is the same move 2. ... d5, which provides black with the sort of advantage white might hope for with a good line. The leakiness of white's kingside is visible with this poorly timed second move as it is with 2. g4??

But 2. c3 forever cements white’s control of the center

While it is respectable, black has fully equal results against the Alapin.

The proof of any move is in the results it gets. Play 2.g4 in as many games as you can and come back and tell us about it.

Mr. Bluestone: Why are you taking umbrage? And what, precisely is umbrage? I have not said a word against g4 is any form, I merely suggested that the OP play the move in a bunch of games and then come to his own conclusions. The scientific method!

"Umbrage is kind of like aspirin. When some people get a headache, they take aspirin. I take umbrage."

Good one!

I always think of umbrage as a kind of combination of humming and outrage

That's a bad arbiting decision. (A good arbiter would rule that the king had been touched with the intention of adjusting it on its square, and thus the touch-move rule would not apply. Said arbiter would also rule that white had been trying to gain an unfair advantage, and apply some sort of penalty. Two minutes off white's clock would probably do the trick.)

This shows how having a rationale that makes sense is not enough to make a line good.

LC0 assesses 1. d4  Nf6 2. g4? to be the 25th best for white in the position. The two moves that are assessed as clearly worse than 2. g4 are 2. Bh6?? and 2. Kd2?. The Omega gambit 2. e4? is viewed as just slightly worse (I have just learnt the name of this bad line).

So, I did quick analysis with Lco for 400 kilo nodes, the winning chance statistics are like that!