For encryption, we want identical plain-text's to encrypt to unique ciphers, also called Semantic Security.
For Signatures, the plain-text (i.e. message hash) is not a secret. The plain-text, if you can call it that, is publicly known. We don't need Semantic Security. There is no “plain-text”, so to speak. We aren’t encrypting.
So do we actually need padding in RSA Signatures? Does padding do more than make it harder to infer information about plain-texts (which is why we usually add it for encryption)? Or is it more of a, "well, it doesn't hurt?" situation?
What is the theory behind adding padding (PSS, PKCS, etc) to signatures?
Note: There is an existing question of similar title, but the question's body does not ask what the title asks.