The transaction fees go to the miner who originally created the block, not just any miner who processes the transaction, and with increased difficulty to find new blocks, it's less likely for new miners (without paying for some really nice hardware) to ever see a cut of the transaction fees.
If there were to be fewer miners to the extent that transaction time becomes a problem, people will attach higher fees to transactions to get them to complete quicker, which increases the profit from mining, which makes more people want to mine, etc. etc.