At a traffic stop the police have the option to require you to present documents at a police station within seven days if they think something is fishy.
And people do seem to exist quite happily without formal identification. As someone who has always had a passport and driving license it was a bit of an eye-opener to me, but if you don't drive and don't travel, some folks just get by without.
So if there is a requirement to have a Britcard, and to present your 'Britcard' when stopped for any reason, then it is definitely a change.
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.