If you presuppose that the purpose of trading is to make money in and of itself then sure. Of course the real (original?) purpose is more tightly coupled to reality and to real goods exchanging hands. There seems to be a fundamental difference between profiting from the exchange and profiting from the mechanism of exchange.

I'm not asking for how we ended up here. I get that faster = better and 1ms faster is still 1ms better. What I'm asking is what value it brings to the world — specifically the world outside of, historically, the pit, and today, outside of the computers executing trades.

Are goods more accurately priced? Is there more liquidity in the market? Is the market more stable? Is the market more efficient, or is it only the technical implementation of the market that's made more efficient by these? Do these benefits, if they're present, outweigh the cost of things like flash crashes caused by algorithms? If flash crashes hurt all of us, then shouldn't we all be benefited by the algorithms when they're doing well? Do we benefit and by how much?

This is why people want "nerdy HFTs" to be taxed in a special way. Maybe it's because they can't articulate the value or maybe it's because there is no value. I can't see the difference and I can't get anything other than evasive comparisons when I ask what the difference is.