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Arbitrage definitely adds value to society. Without arbitrage, traded assets could exist with arbitrary values.

The process of arbitrage involves observing a mis-priced asset and then making a profit from that observation. By doing so, you push the asset towards its correct value. This kind of activity maintains the integrity of a market.

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It does up to a point. I think we're well beyond that point, when people pay for microwave relays to get a few milliseconds of arbitrage, because light is faster in air than in fiber. If someone ever drills a hole through the earth's core, it will be traders looking to save latency between New York and Hong Kong (kidding, I hope).

Yes I absolutely believe that there are diminishing returns associated with arbitrage. I would personally think that exchanges should put some lower limit on the 'time resolution' of their markets to prevent HFT investment beyond a certain point.

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