Eh. In most states you are required to get a new DL if you move. So, in fact, you have to tell the state where you live.
Whereas with a national ID, that wouldn't be tied to a place of residence.
Why would you assume that? our current substitute for a national ID (state issued ID compliant with the federal REAL ID Act) requires current address, and has higher standards for proof of address than many pre-REAL ID state IDs did.
Not really. I file my tax return and the address isn't where I live. It doesn't have to be, it's a mailing address.
Conversely, the most common state ID (driver's license) is effectively mandatory to carry at all times for most Americans because it is required to drive a motor vehicle and driving a motor vehicle is required to move around outside of major urban areas.
I don't want to government to know that much about me. It has been proven over and over that less is better.