if some sort of Stealth address or HD wallet root was the identity gaining the reputation, then address re-use wouldn't have to be mandatory.
The identity would be the X.520 name in the signing cert that signed the payment request. It doesn't have to be a difficult to obtain cert. It could even be self signed for this use case, but then you lose the security benefits and a key rotation would delete your reputation, so in practice I think most people would want the reputation to accrue to the name itself.