It doesn't need to go to infinity. GameStop just needs to get to parity with totality of the collective assets of every short seller. Then to make good on their debt, those entities will be fully liquidated.

They took on unbounded risk and have no leverage if all of the stockholders refuse to sell for anything less.

The stock is less a company than a contract that can be purchased that says the other party has to pay you any price you set (assuming the stockholders are able to hold until the shorts must close their position).

There is a lot of assumptions there. You're assuming the short sellers must cover their shorts at the highest possible price instead of, you know, waiting a day or two. You're also assuming that GameStop doesn't issue any new stock which is already not the case for AMC.

I'm not assuming anything, I'm just asserting that it's a rational strategy that has a possibility of succeeding.

Can the short sellers stay solvent long enough to wait for the price to drop? Short squeezes can last for weeks. The answer is already no, at least some of them cannot, e.g. Melvin Capital