HN user
Yes, that's how firms on Wall Street make money: they exploit inefficiencies in the market in the short term or long term (and, by the way, by doing so, correct the inefficiencies). Paradoxically, firms that target the shorter term do better when volatility is high, because it usually means there are some pretty massive inefficiencies going on.
Re "penny a share transfer tax", the UK already does this, it's called the "stamp tax." Unfortunately, they exempted a few large institutions from the tax, so everyone trades derivative instruments managed by these institutions who don't pay the tax. You only pay the tax if you're stupid.
HFTs and hedge funds are very different entities. If you want to blame someone for man-made crashes, blame the people with large capital outlays, who are forced to unwind their positions when the equity goes down (or up) enough, thus further exacerbating the movement.