Yeah - to be honest, I'm not sure what to make of this because I was not able to follow the math.
From what I gathered, the author is making a claim that, based on his mathematical model, the fees required to secure transaction on the bitcoin blockchain (or any POW blockchain for that matter) are so large that they place an limit on the economic value that can be secured by them. For example, he makes a claim that a $1M transaction would required over $10K in fees to secure, and that because $1M transactions are being secured on the chain at this fee, this is the same fee that would be required of smaller transactions. And because smaller transactions do not work, the chain cannot be used as a store of value. How he justifies that jump isn't clear to me.
It's similar to arguments we've heard from Roger and others that if fees price out small transactions the whole chain isn't valuable. IMO, the vision of lightning is meant to change this and the author does not explore in any detail how layer two technologies impact his conclusions.
I'm left wondering what to make of the paper because I can't tell if i'm just not getting it because I'm not doing the math or because he's looking at Bitcoin wrong, or both.