Whats not in it for China? Breaking the anti China coalition the US is trying to build is reason enough.
It's long-term India management. You can use military force to break the Quad, but the Indians will still be pissed off. Using caste-based movements provides China with at least a friendly country to its southwestern flank.
I'm not saying it's wise to rule out just breaking the Quad by breaking the Indian Army, but I'm saying even when you do that you still need a friendly or neutral India to your side.