That doesn't work without the attesting authority knowing what you are doing, which would make this scheme no longer anonymous.

It does work as long as the attesting authority doesn't allow issuing a new identity (before it expires) if the old one is lost.

You (Y) generate a keypair and send your public key to the the attesting authority A, and keep your private key. You get a certificate.

You visit site b.com, and it asks for your identity, so you hash b.com|yourprivatekey. You submit the hash to b.com, along with a ZKP that you possess a private key that makes the hash work out, and that the private key corresponds to the public key in the certificate, and that the certificate has a valid signature from A.

If you break the rules of b.com, b.com bans your hash. Also, they set a hard rate limit on how many requests per hash are allowed. You could technically sell your hash and proof, but a scraper would need to buy up lots of them to do scraping.

Now the downside is that if you go to A and say your private key was compromised, or you lost control of it - the answer has to be tough luck. In reality, the certificates would expire after a while, so you could get a new hash every 6 months or something (and circumvent the bans), and if you lost the key, you'd need to wait out the expiry. The alternative is a scheme where you and A share a secret key - but then they can calculate your hash and conspire with b.com to unmask you.