There are numerous interesting and/or problematic aspects of this, but this question is perhaps the least interesting.
If your kid, or anyone else really, steals your ID then age verification is the least of your problems. They could transfer all your money, move house, get married, change your name or a myriad of other much more serious things. Willingly letting your kid use your ID would be borderline illegal and not an insurance in the world would cover it.
> literally over 2.5 million
These people have never borrowed a book, visited a doctor, paid taxes or opened a bank account? There are many things in society that require validating who you are. Surely they have some form of ID. Perhaps just a more insecure one than a cryptographically signed.
I don't think a federal identity is as far fetched as you make it sound, for better and for worse.