The author is quite the reductivist. He may well be right but it has to be understood that something like Proof of Work (PoW) is not a permanent fixture. I don't doubt that BTC may very well adopt Proof of Stake (PoS) or something similar once mining stops. And even if they don't, when we reach the maximum limit in BTC, introducing a permanent deflationary state, the mathematical/financial theories nearly ensure value of individual units of the asset become more valuable due to the scarcity factor (so long as the asset is still valued in some fashion, something I assume to be true, at least for this argument). So long as the asset value rises, fee returns will grow as well.
Due to the cost/reward factor once no more coin is generated, the number of mining operations will dwindle and difficulty variable will drop as a result of reduced computational activity on the blockchain. The overall computational load would eventually reach an equilibrium where those miners that stay will eventually see a positive return for their service while many others may flee due to a net negative return. While it may be unfortunate that that most likely results in mining consolidation, it has been witnessed in the past that when any single miner -- or singular entity operating as a pool of miners -- gets dangerously close to a 51% majority of computational shares, the miner community responds to quickly avert the threat due to the very risk that poses to the entire blockchain. I'd expect that as the mining load drops and some entities start consolidating the total amount of shares, other entities will respond in earnest.
But I also strongly expect, perhaps hope, that the developers will begin to start pushing to move on from PoW as the core metric. Whatever they get will surely help give Bitcoin a chance to stick around for the long haul, so long as it's not PoW till the end. The instinctual hunch is to assume the major mining players and pools will fight any such change from what currently exists, but there will come a time where it may very well mean the death of the entire Bitcoin project if they remain the course and that may scare enough miners to vote for change so that their current holdings don't tank in the future. Protecting their own investment may very well scare enough miners to seemingly vote against their own interests, but that's only considering one aspect of their overall interests.
Personally, I think I'm more a fan of Proof of Importance (PoI) over PoS, but it remains possible to convince me otherwise. No matter what, PoW has no long-term opportunity for survival. Until there is free power from something like fusion.