Proof of stake is as equally expensive as proof of work. The trick is that both of based on burning money, proof of work burns by using CPU cycles while proof of stake burns through lost interest.
The problem is that the claim that nothing is as cheap as proof of work as made in that article is only applicable if you think cryptocurrencies have value in a way that is comparable to tangible goods in reality, like the electricity they burn to have proof of work.
I don’t. Your “lost interest“ on a currency that has nothing beyond speculative value is literally worthless to me. The increased energy production and subsequent pollution that proof of work costs, however, has a real value and does real damage to the environment.
Proof of work currencies need to be shut down, for environmental impact reasons if nothing else. You keep playing with your speculative assets all you want. I don’t subscribe to the idea but it doesn’t bother me, until you start damaging the real world with it. Then I have to insist you stop.
You can have whatever values you want, but it remains a fact that cryptocurrencies can be sold for real money and they can be lent at interest using "DeFi" so forgone interest is a real thing that can be calculated.
http://www.truthcoin.info/blog/pow-cheapest/ gives a nice discussion of how this works.