I suppose he actually compared the costs of mining with the costs of minting paper money? Because that sure seems to missing...
It's akin to Facebook's security system. It works the same regardless if it's 100 million users or 1 billion users.
Silvio Gesell explores this concept in depth: https://www.community-exchange.org/docs/Gesell/en/neo/
First: Coins are minted, paper money is printed. Second, and more significantly: Most US dollars in the money supply are neither paper money nor coins, so the cost to mint or print money is pretty much irrelevant to the cost to create dollars.