Your argument would indeed disprove the multiverse hypthothesis, but it would also disprove all of…
Given the current state of knowledge, we cannot disprove the multiverse hypothesis. We can only argue that it is a bad idea, which is why…
Your argument would indeed disprove the multiverse hypthothesis, but it would also disprove all of quantum mechanics as well. The Principle of Least Action is only an approximation from classical physics. Quantum physics follows something like the principle of "almost" least action, in that it has a distribution of paths around the least action path with those closest to it being more likely than those farther away. It is really this that gives rise to the multiverse hypothesis.
Given the current state of knowledge, we cannot disprove the multiverse hypothesis. We can only argue that it is a bad idea, which is why arguments both in favor of and against it seem wanting.