We already have ways to verify identity without IDs, you just don't think about them that way. The entire internet is built on them.

For important things like driver's licenses or voting where everyone has an interest in your identity being confirmed, we could have a federation of identity verifiers which you could voluntarily choose between, and which maintain trust between each other and with their members. That way you can choose one you trust who says to everyone else "yup, this person is licensed, etc."

Very similar to how the fediverse works.