"CBCrypt deterministically generates a public/private keypair unique to each specific user, on a specific server, using a specific password. Any variation of any of these factors results in an entirely different and unrelated keypair."
If it deterministically generates a keypair from a password, then attacker acquiring a public key is equivalent to acquiring a password hash — the public key now becomes a verifier.
"The worst attack a malicious server can mount is an expensive brute force attack, attempting to overpower the rate-limiting function and eventually guess a password that recreates the exposed public key."
Almost the same result as if the server just stored an scrypt hash, but more complicated, and without a random salt. The solution for the problem just makes it worse.