Axiom of Choice cannot matter to humanity in concrete ways (except as an artistic activity), because the Axiom of Choice only applies to uncountably-large sets, which have no realizable physical meaning in the Universe.
Of course. It’s not clear that the “real” or even “natural” numbers meaningfully correspond to any physical phenomenon. They’re just abstractions and tools for making predictions and reasoning about our experiences as humans, which don’t necessarily reflect how the world actually is.
The universe is uncountably infinite; that people routinely stumble over this is why Zeno posed all those paradoxes about motion. In a sense, if you don't believe that reality is uncountably infinite, then you believe it IS possible to square the circle. This actually matters a great deal, since it impacts on things like, what are digital computers (which is to say, set theoretic theories of math) capable of?
Axiom of Choice cannot matter to humanity in concrete ways (except as an artistic activity), because the Axiom of Choice only applies to uncountably-large sets, which have no realizable physical meaning in the Universe.