If the private key is in a smart card, why not? Some countries like Estonia include smart cards in their national IDs.
For those in the US who don't want a national ID: it wouldn't have to be one if the states issued their own. Yes, this would mean they'd all need the technical capability to operate a CA securely. Fund them enough to do that.
The US desperately, desperately needs a proper solution where "thing you give tons of people" isn't also "exactly enough to steal your ID".
As a curious factoid, in-between the world wars, it was popular for workers to have their ID number tatooed on their arm.
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.