My understanding is that there is a very large difference in scale between ratio of trades to portfolio size between an HFT and a mutual fund, such that a tax on each trade would represent a very large portion of the income of an HFT and a comparatively small portion of the income of a mutual fund. Clearly nobody in the financial industry wants a transaction tax, full stop, because it would definitely cut into everyone's profits. There are plenty of profits on Wall Street to go around though, and apparently Wall Street gets bailed out by huge infusions of taxpayer cash when they screw up (and they all keep their giant bonuses afterwards). So, a financial transaction tax is a sort of a Pigouvian sin tax that both deters harmful behavior (HFT) and provides the taxpayer with an income stream that bears some relationship to the implicit guarantee that the taxpayer is extending to the industry.
I've pretty much reached the limits of my knowledge on this, maybe other posters have some more in depth knowledge of other possible policy responses to HFT.