Theoretically, a company in each country could do the same thing. You wouldn't want multiple competing companies in a country with overlapping databases, though, because it'd be way easier to just use your other-company identity to get a duplicate account. (It'd be like using your Facebook account to register once and then your Google account to register again.)
And because of that, any company that did this would have a sort of natural monopoly. So the respective government would have to at least regulate them a bit to avoid them exploiting their users. A "crown corporation", in the British terminology. (In British Columbia we have ICBC, a crown-corporation insurance company, as the issuer of physical ID, which works well enough.)
And because of that, any company that did this would have a sort of natural monopoly. So the respective government would have to at least regulate them a bit to avoid them exploiting their users. A "crown corporation", in the British terminology. (In British Columbia we have ICBC, a crown-corporation insurance company, as the issuer of physical ID, which works well enough.)