I envision replacing the state's central ID databases with a federated system of ID verifiers who have trust among each other and who are run by their members democratically. That way you can choose a verifier that you trust to keep your data private but can vouch for your among broader society.
Very similar to the way the fediverse works. I have my account along one instance, but other instances allow my identity as LibertyLizard to exist as a quasi-account elsewhere so that I can interact with everyone, and so everyone knows I am me. However my true identity does not need to be known for this to work.