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It doesn't seem wasteful and unproductive, given that the result of the HFT industry is smaller bid/ask spreads (lowering costs for all trades) and payment for order flow which is the mechanism that eliminated retail commissions and provides price improvement on many retail trades. And even so, HFT firms are making money.

It might not seem like real work, but making money by reducing costs of market participants sounds like a good thing. I admit though, block trades might be harder now than before the rise of HFT.

If you could do warehousing/distributing/coordinating fresh foods in a way that reduced the difference in price between the farmer and the consumer and make money doing it, that would clearly be good work.