Follow-up on the previous post. The "commit to a ledger" part requires for the user to be able to prove their identity to the ledger, which is trivial if it is centralized, but if the ledger is a blockchain, then this essentially means that the user must hold long-term cryptographic keys which allow them to commit messages about their identity onto the ledger. (Enumerating the potential consequences of being able to post spoofed identity notification messages are left as an exercise to the reader.)
But if the user has long-term keys, then I don't really see a point in maintaining an out-of-band ledger of identity changes and not instead tying the keys to the BID directly via posts to the specific timelines, signed by those keys.
Such an approach smells awfully similar to Salmon and its Magic Signatures, as seen on, say, Diaspora.
Also an interesting case study is Scuttlebutt, where one's identity is tied exclusively to their control of cryptographic keys, and there's not even really a concept of a "provider" per se.
The only reason why I can see a blockchain being useful is when fully serializable and centralized BID ↔︎ PID mapping is required. But I'm not sure under what circumstances this would be needed—I can only think of discovery (essentially building a huge list of all users of @bluesky) as a potential use case.
If Bluesky decide to reinvent the wheel, I really hope that they'd cite enough prior art, because if their problems will have been solved by ActivityPub and the like, that'll be a bad look. But not that my humble opinion matters, what with me attempting to become less of a Twitter user :)
(For what it's worth, I did get my account back, and I still continue to intend to use it much less.)