There are lots of ways to implement identity verification while preserving privacy. It's actually a super interesting engineering problem. Estonia has an excellent model to build on. The government can maintain a "traditional" ID system based on documents and in-person verification, and provide you with a device similar to a yubi-key or Bitcoin hardware wallet that could be used to share specific, cryptographically verifiable claims with third parties, like your age, or even just a boolean "over 18", but also your name or other information if you choose, with a way to control the access and audit which parties have verified which claims with the govt.
In Poland online banks to that. You can verify your identity for government purposes with the use of your online bank. No need for government to set up a scheme to confirm millions of people in person.
govt, banks, whatever. I don't care who administers the system as much as I care about the fact that they're highly regulated, and you have the control needed to expose as little information as necessary to confirm things about yourself to third parties (like just "over 18" for many sites, or your full identity for other things if necessary).
