> In my view nonnegative real numbers have good physical representations

In my view, that isn’t even true for nonnegative integers. What’s the physical representation of the relatively tiny (compared to ‘most integers’) Graham’s number (https://en.wikipedia.org/wiki/Graham's_number)?

Back to the reals: in your view, do reals that cannot be computed have good physical representations?

Good catch. Some big numbers are way too big to mean anything physical, or exist in any sense. (Up to our everyday experiences at least. Maybe in a few years, after the singularity, AI proves that there are infinite many small discrete structures and proves ultrafinitist mathematics false.)

I think these questions mostly only matter when one tries to understand their own relation to these concepts, as GP asked.