The author is a critic of continuous limit-order book markets for what seems to be a different reason: as the interval at which things trade constricts, correlations can break down between things that should be priced 1:1.

His best example is ES and SPY, two different ways to trade the S&P500.

There's a straightforward high-frequency arbitrage strategy to deploy against that problem: if ES or SPY is "mispriced", trade in offsetting amounts, in the expectation that the correlation will be restored (as it must eventually be). In Budish's view, this trading is a needless cost that doesn't improve price discovery.

I'll just say, that's not IEX's argument against HFT.