Is it specifically the fact that it's a physical process that makes it earth shattering?

Physical models of computers ( https://en.wikipedia.org/wiki/Billiard-ball_computer ) have been around for a long time, which means that noncomputability has been tangible for a long time.

I might be numb, though, to the fact that much of what want to understand can't be. If the universe isn't discrete, then it seems like noncomputability is the default.