There is an inherent problem with BIP120, Proof of Payment: If there is a soft fork, a server that verifies PoPs will accept a PoP as valid without checking any of the new Bitcoin rules.
For example, a server will be fooled by a segwit transaction, because the server doesn't have a witness to verify and consequently will accept any PoP with an empty scriptSig.
Since BIP121 depends on BIP120, that has to go too.