Second Look at Weak Blocks

So if I understand this proposal, the problem is:

Divergent mempools due to local mempool policy across the network increase latency for block relay.

To solve this problem, this proposal introduces another data structure (could you say PoW Mempool?) that holds a set of transactions that miner is attempting to actively construct a block from?

If I understand correctly, this would increase resource requirements for running a node (-maxmempool would be circumvented?), for the benefit of reducing block relay latency.

Maybe to end with a controversial question, could this just replace the gossip based mempool (in favor of the PoW Mempool) in the future? What ramifications would that have for the network?