Is that not simply hypermodern school with the fianchettoed bishops?
Other pro tip: if you do the full hippo with all the fixings (double fianchetto, pawns e6 d6 h6 a6) it also allows you to delay castling until you know which side your opponent commits to. This can lead to an awesome attack that comes out of nowhere and completely blindsides the hippo-unaware.
1. If they castle one side, you can do the other and then launch an attack, usually it’s the pawns that clear the way and open lines, then rooks and minor pieces can get in the action. (As opposed to using rooks to push down pawns, if I’m reading your comment correctly)
2. You can also see if they are preparing an attack on one side, usually watching pawn structure or where they’re putting rooks. And then you can castle on the opposite side to effectively neutralize the attack.
Note that it’s definitely possible to launch an attack on the side you are castled on, especially if the center has a closed pawn structure - it’s just more risky and thus less common.