If the transaction hasn't been committed (etched into the blockchain), then isn't there a financial advantage to accepting the highest fee transaction? The pro

If the transaction hasn't been committed (etched into the blockchain), then isn't there a financial advantage to accepting the highest fee transaction? The protocol doesn't matter, mempools aren't validated or shared[+], and so the validity of the chain isn't challenged by processing the higher fee. So given that the bitcoin network is designed to be operated by greedy miners, surely one would break with "tradition" and process the second? You might have to dig to find a route to those nodes but it should surely be possible. [+] They're not shared as in shared-state, i.e. sync'ed.