I think the opposite! The problem is that almost everything in the universe can be cast as computing, and so we end up with very little differentiating semantic when thinking about what can and can't be done. Busy beavers is one of a relatively small number of problems that I am familiar with (probably there is a provably infinite set of them, but I haven't navigated it) which are uncomputable, and it doesn't seem at all relevant to nature.
And yet we have free will (ok, within bounds, I cannot fly to the moon etc, but maybe my path integral allows it), we see processes like the expansion of the universe that we cannot account for and infer them like quantum gravity as well.
And yet we have free will (ok, within bounds, I cannot fly to the moon etc, but maybe my path integral allows it), we see processes like the expansion of the universe that we cannot account for and infer them like quantum gravity as well.