The cow is out of the barn and half-way to Canada.
So why slam the barn door now?
We have to produce State IDs, credit cards, SS cards, birth certificates (not photocopies), passports, pretty much any time someone requests them. You have to be a hermit to get by in our society, without producing proof of who you are.
Furthermore intimate information on us is housed all over the place and freely available. The places where this info is protected, are rare, and guaranteed only by a promise or statement of intent from the info holders not to share.
I don't know what you think can be done with national ID that has not already been done?