If the government decides it's not in the public interest they can stop it. At least they should tax it so as to extract the maximum revenue. E.g. 0.1% on every transaction, waived if you hold the instrument more than 10 minutes.
Bro, that's not how government works.
Government stops things that it perceives are not in THEIR interest.
As long as they keep getting bigger campaign contributions from the people making billions on HFT than from the small guy looking to be protected from HFT, it will continue to exist.
Also, a simple tax wouldn't be enough, look into the CFDs created to get around the UK's stamp tax (tax on stock transactions).
It would be passed as a gesture to the small guy while the real game is allowed to continue.
I'm not really sure why the SEC hasn't banned HFT yet.