I wonder whether this problem can be mitigated by signing tweets with cryptography signature. Then people can put the public key in the blockchain or third-part

I wonder whether this problem can be mitigated by signing tweets with cryptography signature. Then people can put the public key in the blockchain or third-party websites. The user can sign the message with their private key and other people can verify it with the user's public key. So if the attacker can gain access of Twitter system, at least they can not forge the message. But of course they can do other damages, such as reading private messages.