That is very surprising. In the US, you are legally required to carry your license when driving. If you are caught driving without one, expect to be arrested.
That should only be for non-citizens, but I have no idea how you could prove that without documentation in the first place.
So for the vast majority of Americans, you probably have to be carrying ID at all times anyway, else you risk someone deciding you "might" not actually be a citizen.
If this same rule was enacted in the UK, there would be no place on the British Isles that would be excluded, as nowhere is more than 100 miles from the coast.