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.