You can't just transfer a process/technology that works in Estonia to a country like the U.S. which has 300x the population and decades of processes that are dependent on SSNs, many of which aren't controlled by the government.

Want to open a bank account? Need an SSN. Healthcare: SSN Employment: SSN

Want a STATE driver's license? Need some form of government ID, depending on the state. An SSN card is often an option.

My point is, to adopt a system like you suggest would require reforming ALL of these systems across public (federal, state and local) and private sectors.

It's not just bureaucracy. Doing this at scale across public/private domains is hard.