The primary aim of introducing weak block propagation is not to synchronize mempools but rather to enhance the relay process. This clarification indicates that the focus is on improving how blocks are relayed across the network, rather than ensuring all participants have identical sets of unconfirmed transactions (mempools).

There's a notable distinction made between the objectives of weak block propagation and mechanisms designed to encourage the disclosure of "hidden" transactions. The latter refers to strategies or technologies that incentivize participants to share transactions that they might otherwise keep private, for strategic or financial reasons. The conversation brings to light a sense of confusion or skepticism regarding the actual benefits of adding a Proof of Work (PoW) header to weak blocks. The argument presented suggests that the addition of a PoW header, a component integral to the validation and security of blocks in blockchain networks, does not evidently contribute to enhancing block relay. This point of contention invites further explanation or justification on how weak block propagation, especially with the inclusion of a PoW header, effectively improves the relay process without addressing mempool synchronization or the publication of hidden transactions.