From what I've read on Wikipedia [1], my guess would be that the answer is probably: "Since it's impossible to falsify, we should only be satisfied with it if science can eliminate literally all other possible falsifiable explanations." In which case, I guess if your goal is solely to "push the boundaries of science", then this is fair enough. But in that case, it seems to me the amount of effort and resources we could ostensibly pour into eliminating falsifiable explanations might well be unlimited, which raises the question of: at precisely what point do you cut your losses and realize you need to move on (to philosophy? idk), so to speak. Science is supposed to be a means to an end, after all, and I thought that end was "understanding the universe"—not "exploring the space of all falsifiable predictions just for the sake of it".

But I'm curious to hear physicists' takes on this! e.g., the implausibility claim in the Wikipedia article would seem like a compelling rebuttal, except that I don't see why I should believe superdeterminism to be an implausible explanation at all. If anything, it sounds like the most plausible explanation we have—either that, or the Big Bang somehow doesn't imply superdeterminism (how is that even possible?), or the Big Bang theory is bogus to begin with.

[1] https://en.wikipedia.org/wiki/Superdeterminism