Indeed! And in fact, there are set theorists who argue that the traditional dream solution to the continuum hypothesis, adopting new axioms, is doomed to fail,

Indeed! And in fact, there are set theorists who argue that the traditional dream solution to the continuum hypothesis, adopting new axioms, is doomed to fail, and that we should instead embrace all models of set theory, all possible universes of mathematics. I tried to write an introduction to this "set-theoretic multiverse philosophy" which is accessible to the HN crowd here: https://iblech.gitlab.io/bb/multiverse.html https://iblech.gitlab.io/bb/multiverse.html