The standard justification is that these firms provide market liquidity which lowers the cost of capital for all businesses, thus boosting economic growth. But I've never seen a rigorous quantitative analysis. How much growth do they actually cause in the real economy relative to the value they extract?
Being one microsecond faster is worth all the profit, but did the market gain as much with one microsecond less latency as with 1 second or one minute less latency? No. But the payoff for achieving it is just as high, winner takes all to whomever is fastest, so the market will put as much money into shaving off an additional microsecond as a minute, if it makes the difference on being first.
I can see where you're coming from, but it's important to remember that what they are competing on is not only time but also spreads. Spreads have tightened substantially over the past couple decades thanks to these firms [1], which means that the total amount to be made per trade has dropped significantly. On top of that, the landscape has become so competitive that trading firms are now purchasing order flow, which basically subsidizes broker commission fees for trading. This is a huge win for retail investors, as the cost of trading has made it much more accessible -- in the past you would have had to buy many more shares and make a much higher return to offset these additional costs of trading.
It's winner take all for whoever has the shortest path (for something like index arbitrage). There is no value added to anyone if another competitor invests millions in microwave relays or custom hardware parsing to snipe the previous low latency winner and beat them out. It's just wasted money, other than knock on effects of more demand for hardware growing the hardware industry faster.
