You're right, all the websites could band together to coordinate and share that the same person logged into each site. They do this today with email addresses and phone numbers explicitly (and implicitly with "advertising IDs" and the like). The Facebook "like" button and Google analytics are both tools to make it easier to track you around the web. Getting away from being able to track you around the web is going to take a lot more than just an anonymous ID as your login credential.
That said, the unique identity is still valuable--Apple offers this with their third party sign in[1]. Practically, if everyone was using self-hosted identity, then the tools would probably make it easy for you to create and track your own new identities for each service you use. This isn't build into something like IndieAuth today, but with the right DNS settings you could have arbitrary subdomains return the same authentication options and act as easy-to-use "sub identities".
That said, the unique identity is still valuable--Apple offers this with their third party sign in[1]. Practically, if everyone was using self-hosted identity, then the tools would probably make it easy for you to create and track your own new identities for each service you use. This isn't build into something like IndieAuth today, but with the right DNS settings you could have arbitrary subdomains return the same authentication options and act as easy-to-use "sub identities".
[1]: https://support.apple.com/en-us/HT210425