Privacy Concerns: Vanity addresses, by their nature, can reveal a portion of the private key during the generation process. This could potentially expose users to security risks if the process is not handled properly. Caution must be exercised to ensure the private key is adequately protected.
That is rubbish. If you generate a private key, create a public key out of it, give the vanity generator only the public key, and tell it to generate another private key its public key that creates the vanity address when the two pubkeys are added together, they will still be able to find the vanity address because they must add the two public keys together, but they will not be able to create private key for that vanity address because it only has its own generated private key and not your own private key which it needs to be able to add it together to get the real private key.