Maybe so, but some information is safer to reveal than others

Option A: the receiver gives the sender a one-time payment string, the sender pays it, and the the receiver irrecoverably discards every trace that he ever had the payment string

Option B: the receiver gives the sender a reusable payment string, the sender pays it, and they both keep the string forever

The latter is worse for privacy because the shared piece of data ties the sender and the recipient together, it stands as an everlasting proof that they interacted. At least one of them should discard it because if it is found on them both, it is evidence that they once interacted. But there is only one way for each to be sure that at least one of them destroyed it: destroy it yourself.

This is not encouraged in monero; on the contrary, the standard contact list feature encourages the sender to keep the receiver's monero address and reuse it, and the standard recommendation for the receiver is never to delete his private keys, because someone might send him money at an old address, not knowing he deleted the keys.