Authentication in Denmark also uses cryptographic signatures etc.

The CPR alone is used for casual identification.

Personal numbers and social security numbers in US are horrible idea, essentially a password and username simultaneously

Just to expand slightly on this: Some old procedures, probably from the main frame age, live to this day in old institution, including the belief that you can ask people about their personal number over the telephone and auth them that way.

I don't think any IT infrastructure is doing it, it's all by a national single-sign on system.