1. They Provide liquidity, false. Or at least works on a definition of liquidity that is not what would generally be used by other market participants (institutional or retail) - specifically see pinging or using orders to determine interest [2]
2. Tighten spreads, false. Attributable in the largest part to reg NMS not directly to HFT. Spread volatility has increased.
3. Lower costs, false. Cheap trading available via discount brokers before HFTs and additional costs to other market participants operating in HFT innundated environments are ignored.
4. Studies showing positive of HFT cherry pick and are of inconsequential detail, no conclusions should be drawn without deeper analysis of the data
5. Nannex guys just have an axe to grind repudiation
Plus ignores any other negative side effects of super-high speed trading such as stock specific flash crashes, data overload, and locked / crossed markets. Appreciate some of those can also be attributed to the proliferation of protected markets post Reg NMS.
[1] http://www.nanex.net/aqck2/4594.html [2] http://www.nanex.net/aqck2/4592.html (appearing to violate SEA 9.a.1.A)