For true privacy you need to be sure it can only be released when BOTH people agree to release it.
If for whatever reason Bob does not want it known that Alice paid him if Alice can release in unilaterally then it's not really that private.
It's also not that useful, as payments can trivially be denied by a fraudulent receiver, with no recourse for the buyer.
Payment proofs are a critical component to a functioning economy bases on digital payments.