Under the headers first scenario, wouldn't the full block still reach everyone in the same time as it would under the current rules?  So the small miner loses nothing in terms of updating their UTXO set, but gains an early "heads up" alert that a new block is coming.  This allows them spend the propagation time working more productively on an empty block in the new chain rather than wasting time on an orphan.  It's true that it doesn't solve the problem of larger pools vs smaller pools, but if it doesn't make it any worse then headers-first propagation would be a net benefit to the network since it removes the incentive to make small blocks.