If the only way to associate a user with their ID is by fingerprinting them, you can do the same thing without an ID with having shadow profiles. If the proof system is designed for privacy, the ID doesn't make you more trackable.
In other words, if the ID never directly leaks companies can just make up a static ID for you and get the same results.
There is a permanent ID, but it doesn't have to be told to the site.
In which case it doesn't make tracking any easier than the site making up a "fake" ID for you.
This doesn’t make sense. The whole point of using IDs in this way is in an authenticated context.
Did you think I was suggesting that this ID would be accessible to any website without asking? This is something you would send as part of a registration step. So, for instance, if you spam Hacker News, you get banned, you try to register again, it receives the same ID as before and knows not to let you register.