couldn’t you just collapse all of the entrances to casterly rock, leave a garrison to make sure there’s no tunneling, and come back in six months when everyone’s dead?

That’s one strategy. The difficulty is that Casterly Rock is honeycombed with tunnels already and is geographically massive, so it’d be hard to pull that off. 

Honestly, if I were going to besiege Casterly Rock, I’d cut off the harbor entrance (sinking a bunch of hulks should do it) to prevent resupply from the sea, and then dig a moat around the entire landward side to starve them out.

But even then, six months is a very optimistic projection. Sieges can take a long long time, even without the absurdly spacious storerooms of the Rock.