In a highly competitive market, transaction fees, and more worryingly, the network's hash/s, will converge towards zero.
This is because a miner who discovers a new block only has to pay for the cost of proof-of-work, not for the cost of bandwidth and storage associated with that block.
Absolutely correct, IMO. Classic externalization of costs.
Except as mining becomes less profitable, less people will want to do it, which will lower the difficulty, which will make it more profitable.