I don't want to live in such society. Yes, bad things can and have be done before. But making them simpler, cheaper, and more scalable needs to be avoided.
The much more effective solution here is to regulate businesses in when they can request/use somebody's primary key and/or other PII, and to simply not allow it in any case where a pseudonymous identifier or partial information (e.g. only somebody's approximate age rather than their full date of birth) would do just as well.
And Germans arguably aren’t “forgetting their history”, they are just regulating to achieve desired outcomes (no government and corporate privacy invasion; strong authentication where necessary), not mechanisms (no unique identifiers).
Times and technology change, so why uphold an old (interpretation of) law that is neither necessary nor sufficient to achieve the desired outcome in the present day?
That still does not make it "government information". It's a primary key that (currently) may not be used by the industry. But by itself, it does not identify anything or anyone. In that sense, it's even less sensitive than a name; realistically though, if it's widely stored next to the associated name anyway, it's effectively the same as a name in terms of sensitivity.
A credit score is effectively a database shared across the financial industry. As such, it needs some sort of primary key. That can be either be something globally unique, like an SSN or equivalent, or a wonky composite primary key (first_name, last_name, date_of_birth, last_known_address) which will cause lots of false positives and false negatives:
What if you change your name? What if you move? What if there's somebody with the same name born on the same day in the same city? What if the spelling of your city has changed between your birth and your time of requesting a loan/credit card?
You may object to the idea of credit scoring in general, but being ok with credit scoring, yet objecting to the usage of a sane primary key to do it, makes no sense to me.