Earlier quoted context omitted.
If the private key is in a smart card, why not? Some countries like Estonia include smart cards in their national IDs.
I'm increasingly convinced that this is the way forward. Having a key verifiably tied to you as an individual goes a long way to enabling a broad range of governmental services. Digital voting, for one thing, but also no more need to rely on shady credit check companies for address verification, as I've seen on some (Canadian) government forms.
Using cryptography in addition to "classic" means of attestation sounds a lot better to me. You could also make it an "optional feature" of people's citizenships (like 2FA on an account) to ease adoption.