Relativity means there can never be an objective mempool.
I don't think this is really a problem though. Transaction fees are precisely a bribe to a miner to include the transaction in the block. The mechanism exists, so use it.
The implementation would require folding the p2p-pool mining protocol into the main protocol where it would serve as a sort of proof-of-transmission that is resistant to the Sybil attacks. This has been discussed many times before.
Yes and every time it is discussed it is a dead end because in order to succeed it needs exactly the sort of consensus algorithm that proof-of-work implements. There is no such thing as "proof-of-transmission" as a consensus algorithm that is sybil resistant, at least none that has been shown.