In general, it could be enforced as a random identifier generated with each electronic application; this just burdens employers with implementing an electronic applications system, which is too high a regulatory burden (and would make dropping off a CV in person impossible/illegal, which is stupid.)

It could be a hash of the persons name, too, but then the public would have to learn what a hash was...

NI number works well in the UK, because it's convenient (and the original suggestion was specifically for the UK.) A similar system could be used anywhere.