The problem with a tax is it just becomes a cost of doing business, gets absorbed or priced in, and everything just goes back to the way it was*. A cap on trades is a permanent brake on HFT. How about a frequency cap and a tax? 
* Except education is now better funded, which is a win … at least until the next Republican Prez/Senate/Congress, at which point the tax either gets repealed, or something else has it’s funding cut so the frequency-tax has to stretch to cover that too. Or, given R behaviour in recent years, both.
