I don’t think that’s true? If a miner mines the low feerate “miner tx” before it expires, leaving some random higher feerate txs in the mempool, that raises the fees available in the next block for everyone including low hashrate miners. So I think that actually gives an advantage to low-hashrate miners: they get the benefit of an occassional bonus high feerate tx, without having to pay the cost of having mined a low feerate tx first.
That is: yes, there is an incentive for large miners to behave differently to small miners, but that difference benefits whoever finds future blocks equally, whether they participated in the strategy or not, whether they’rea small miner or a large one.