Whenever I hear about Jane Street and other such trading companies I wonder what do they bring of value into the world. It seems they're basically just working on increasing economic equalities.
1. Market making (providing two sided liquidity in a market), and in general providing liquidity (even one sided) is a real benefit that (some) trading firms provide (e.g. Virtu, but also many proprietary shops).
The market making function solves the time-mismatch between client A who wants to buy now, and client B who would want to sell in 1 hour.
The liquidity provision is what allows, through pay-for-order-flow, retail investors to get the best current price for AAPL through their Schwab app. Not only that, they do not have to worry about the order execution (how long would it take to get filled), and their fees are low or 0 (because someone is paying Schwab for the order flow).
2. A similar, but slightly different trade is what ensures that ETF are priced "correctly". This is also a boon for retail investors.
In order to ensure the ETF price are in line with the price implied by their underlying assets, someone need to do the "index arbitrage" trade. Again, retail gets a nice useful product (e.g. SPY which tracks S&P500) instead of having to buy a lot of stocks (naively, 500).
3. And then there are directional trades, which are basically trying to "arbitrage away" moves in correlated prices. Is there a value in this? Maybe, but it is just accelerating existing trading realities. Someone would have done it anyway.
I am guessing the perception that the industry adds no value is because of stories about the ridiculously low latency number - trade in the blink of the eye, reacting in nanoseconds, etc.
And I tend to agree.
If the exchanges changed the way they matched orders (e.g. instead of First In First Out/time priority ["who came first"]) to a procedure that introduces randomness that eliminated the advantage from nanosecond/microsecond differences, it would make no difference to the world.
The prices would still be "good enough" (no retails participants care if the prices settled within 100 nanosecond, 1microsecond, or 1 millisecond).
So to sum up, does it bring value? Yes, but it does not mean there is no silliness involved.