Only if block sizes are limited. If they are unlimited even a tiny portion of the hashrate can continually clear the market at effectively no cost to themselves, thats the whole point of this post-- creating a cost for doing so.
Why do you think this is a problem, or more specifically, why do think there is no cost to larger blocks in the system I proposed (did you read it?)
If nodes are charging for bandwidth, and those transactions are in the mempool of most of the network, then the people who created the transactions already paid for them to be distributed.
If some miner with 5% of the hash rate includes all transactions in the mempool regardless of fee, then it just means that paying no fee means the transaction takes 3 hours to get confirmed. Anyone who wants a confirmation faster than that will pay a higher fee.
If miners are independently collecting transactions which are not broadcast to the network ahead of time, then they lose O(1) propagation speed. Their block will be more expensive to propagate in terms of direct cost and orphan risk.