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Suppose one of the big mining pools, that holds e.g. 20% of the mining power, creates a wallet software that, by design, sends all transactions only to pool members - and does not relay it to nodes outside the ppol. Will this give them an advantage in getting mining fees? What keeps the big mining pools from doing this?
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What is the point? The service you get as a user is worse, with 1/5th of the hashpower, I as a user have to wait longer to get my tx into the chain.
Now something similar is already happening, and has been for a long time. I can pay a pool to get my transaction a higher priority. Instead of replacing my transaction with a higher fee, i pay the miner directly so they will include it in their next block.
I get it you are thinking allong the lines of ''well if this pool has a part of the mempool that is only exlusive to themselves, they will get that money, but others wont'', yet from a user perspective, it makes no sense to do this. It takes more time, i see no reason why it would be cheaper.
Remember, the systems functions under ''I as a user am indifferent as to who includes my TX into a block, as long as it happens'' & ''I as a miner am indifferent as to what TX's I am including, as long as it has sufficient fee's''.
