What's the win to society to "mitigate" an "incentive"?The main incentive is reducing time and energy devoted to a zero sum game.
A hypothetical: imagine a sunken pirate ship is discovered. Now suppose 10 crews of divers get into a race to retrieve the pirate gold. It's useful to society to bring up the gold. It might be useful to society to have a race between 2 crews to bring up the gold, to make sure the first crew doesn't dilly dally. The gain to society is $GOLD - 2 x $DIVER_COST, or perhaps $GOLD_AFTER_LONG_DELAY - 1 x $DIVER_COST. On the other hand, having 10 crews of divers all competing for the gold is pointless - the gain to society is $GOLD - 10 x $DIVER_COST, which is 8 x $DIVER_COST less than if 2 diver crews chased the gold.
HFT is basically the same situation as the race for pirate gold - a lot of smart people in a race to create a fixed amount of alpha. We might be better off if they were creating new alpha elsewhere instead of all simultaneously chasing after the same alpha.
(That's not to say I'm advocating a ban on HFT on this ground. A certain amount of effort devoted to HFT is certainly a good thing, and I doubt the government would get things right. I just don't think the market is getting things perfect either.)