Sorry, stressed might be too strong a term, I like using overstatement.

I doubt very much that we will see aggregate fees increase to anywhere close to the level that mining revenue is at now, which means that overall the level of available money to miners will decrease over time.

Combine this with power costs and it should lead to a smaller network (some miners leave, others reduce investment) and more efficient hardware that consumes less electricity on aggregate. This is because after the minting operation is complete, 33% of the value of the mining community (to the bitcoin network) is gone, and now it's focus should be on making it's core functions more secure instead of subsidising a larger set of miners than needed. As part of this we will have to redefine a "small transaction" at some point and lower the fees on them proportionately, because having to pay a $5 transaction fee when buying a coffee because BTC makes it up to $1000 is not going to work.

I think large institutions will get into the game at some point and we will start seeing peering agreements that happen outside of the typical transaction fee mechanism. Once that happens all bets are off on fee structure as they are likely to try to eliminate them rather than increase them. That's because large institutions will be able to take a loss on their bitcoin farm (and standby equipment, and ASIC on-demand manufacturer contract) because they can make so much more from the services they offer WITH bitcoin, but they are going to want to minimize that loss.