Why 3 pawns in front of a king (f2,g2,h2 pawns and king on g1) pretty much sucks


I partially agree but thats why you open up space for your king. This is a puzzle of what to do in this case:

It will be difficult to put 6 in front of your king....


Okay good. I believe like you said, g3 then Bg3 is a really good defense for the king. Actually, I am trying to test how will it end while playing with bots since it might be a good opening.
#1
Pawns on f2 g2 h2 offer the most solid defence for a king on g1.
A pawn on h3 can be attacked by g5-g4, or by sacrificial attacks Nxh3, Bxh3, Nxg2...
A pawn on g3 can be attacked by h5-h4 or f5-f4 or the natural defending bishop Bg2 can be traded off by Be6, Qd7, Bh3
A pawn on f3 or f4 opens a dangerous diagonal a7-g1 right to your king Kg1
No one says that castling makes your king untouchable. F2, g2, h2 pawns formation can be broken, it is your task to monitor your opponents threats to your king and neutralize them, king's safety is not only about castling.
But a castled king behind those pawns does tend to be safer than the king in the center or when one of the pawns in front of it has been moved, weakening certain squares and making hooks for attacks and sacrifices.
Of course, this is just a general rule. Every position is unique and sometimes castling can be a mistake.

No one says that castling makes your king untouchable. F3, g3, h3 pawns formation can be broken, it is your task to monitor your opponents threats to your king and neutralize them, king's safety is not only about castling.
But a castled king behind those pawns does tend to be safer than the king in the center or when one of the pawns in front of it has been moved, weakening certain squares and making hooks for attacks and sacrifices.
Of course, this is just a general rule. Every position is unique and sometimes castling can be a mistake.
One of my friends castled, and found that it was a brilliant move.
Reason 1.)Fragile against rooks/queens
Imagine your opponent’s rook is placed on the first rank,your king is check,you must draw at least 1 piece or more to defend it.If there is none,you’re done.You get backrank mated.The solution to this problem is easy though,but it can sometimes waste your attacking material at the same time
Reason 2.)Fragile against diagonal batteries
Its a big issue when your opponent is impatient to checkmate you.When your opponent is threatening kiss of death checkmate capturing the h pawn,you may play g3,but it was a big mistake because a bishop can now go to h3 to cause some problems.Same issue with the g pawn
I wasn’t saying that 3 pawn defend king thing is the worst defense.I rather say its…ineffective.I rather do g3,bg2,Nf3 0-0.