I think reality tends to trump thought experiments. I don't dislike the 1-second auction idea, I think it would work quite well. But I disagree that IEX's ability to stop the HFTs cold is a fluke that will disappear as their volume goes up. Their reasoning is sound and obvious and immediately solves the biggest problem that money managers have these days when trying to buy or sell large amounts of stock. I don't see how volume changes the equation at all.
Besides, his paper does not appear to say what you summarized at least in regards to IEX. It simply states that IEX is solving one aspect of the problem. It's pretty easy to argue that the piece they are solving is the biggest piece of the pie. Personally speaking, I don't care about the aspects of HFT which only involve standard arbitrage.
In terms of HFT... it was obviously fraudulent from the day it started beind used. The SEC should have acted immediately and didn't. Companies were spending hundreds of millions of dollars on infrastructure to get sub-millisecond transit improvements and they were lying to our faces talking about improving liquidity, magically, well in excess of the capital they actually had in play, when it was obvious that they were only exploiting flaws in the system.
It was a failure of the financial media as much as it was a failure of the SEC, but the SEC *should* have acted immediately and they didn't. And the result is a major loss of trust in the mechanisms of the stock market to the point where many retail investors who didn't understand the low scale of the fraud exited the market and stayed out of the market when they should have stayed in. I'm not going to make excuses for those people, I certainly wasn't scared away, but the general public deserves better than what the media and the government has handed to them over the last ~6 years.
-Matt