Isn't there a little bit of 'chicken-and-egg' here?
Why would miners use these new 'efficient schemes'
in the first place if it was to render the fee market
ineffectual, unless they were already relying on something else
(blocksize limit) to do that (support a fee market)?
More efficient block propagation results in higher profits for the miner, so miners are incentivized to improve their communication with the network's hash power. As the network as a whole gets better at block propagation, the "supply curve" falls, resulting in lower fees per kilobyte (measured in BTC) and higher average block sizes, for a given demand curve.
This is a good thing, as it is what will allow miners to produce much larger blocks in the future and as well as allow fees per kilobyte to continue to fall (especially important should the price of a bitcoin rise dramatically).