You're absolutely right that it might not reflect physical reality. I don't think it's known whether space is fundamentally discrete or not. But I can definit

You're absolutely right that it might not reflect physical reality. I don't think it's known whether space is fundamentally discrete or not. But I can definitely say that continuous space meshes a lot more with my experience as a human being, and that because of that, the real numbers are motivated by more than just taking square roots. They model the human experience of space.