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.