I seem to recall reading here on HN a few weeks back how surnames came into existence: it was because the (? Italian) government wanted to track taxes. Before that everyone had several ways of naming themselves: John, John son of Joe, John of someplace, John the carpenter, etc. Personally, I really like that because I'm not just "one thing", but am a person who has different aspects.
You already have one, SSN and similar absolutely count and allow aggregate different data. Not to mention that you're absolutely forgetting about the fact that humans don't have a lot of entropy, k-anonymous data is not what we have by-default. You are wrong about a centralized system "providing a way to aggregate data" it just makes it easier. I live in a country that actually gives citizens access to a centralized identity system and I'd say it has solved much more than you're giving credit for.