I don't think he's saying that miners won't mine at all, just that they won't mine no-fee transactions.
A rational miner mines all non-zero fee transactions he sees until the block is full, since it has virtually no cost to include one. If he would not include any, he would leave it on the table for an other miner.
Imposing lower limit to fee could only be effective if miner build a cartel for that, and this is not the way of regulation I favor.
You keep saying this but the cost is not zero. The cost of orphaned blocks is very real. If you increase propagation time by six seconds then the probability that your block will be orphaned increased by 1%. Those transactions have to be paying more than the estimated loss due to increased propagation delay or the miner takes a net loss. As margins squeeze and the subsidy declines, miners that are bad at math will quickly become bankrupt miners that will be replaced by miners less bad at math.
Another way to look at it is if you double the size of a block you double the chance of your block being orphaned however since miners include highest fee transactions first doubling the size of the block does not double your gross revenue. At some point there is that marginal transaction where despite it having a fee it will result in a net loss to include it. A rational miner will draw the minimum fee policy just above that line.