Will the fees increase by much? Will miners drop out, thus making it easier to mine, thus reducing the fees?
Technological advancement would make mining much cheaper in certain countries. By the time 2140 comes, miners would probably have ROI'd on their last ASICs and they are earning pure profit. There is nothing to lose by keeping them on.
I predict that some ASIC farms would drop out from the race and the mining equilibrium would keep mining profitable. Bitcoin could be worth more and scaling could ensure that the fees/block is substantially higher.