Comment by wavemode

It's much simpler than that. The utility provided by arbitrage is that a given security is no longer under- or over-priced in one market relative to other markets. Any buyer/seller of that security will then always be buying/selling for the best available price (rather than losing out on money by not buying/selling in a different market).

The price discrepancy which was corrected by arbitrage is, itself, the compensation the arbitrageur receives. If it weren't, that inherently also means that there still exists a price discrepancy, and thus an arbitrage opportunity.

This is all separate from the question of public policy. Should taxes on income from arbitrage be increased? Perhaps they should. Though that doesn't affect the mechanics of how arbitrage works, it simply decreases the net profit of the firm doing the arbitrage.

Conceivably, you could increase the taxes/regulations/restrictions on such firms to such a degree that they are either no longer allowed to perform arbitrage at all and/or can no longer justify the cost of the high-speed equipment involved. The end result of this would be that the markets become less efficient (there would be greater price discrepancies and they would arise more frequently).

How much does that matter? Well, that's more of a philosophical question. How much does it matter to you that you're buying something for the best possible price (versus knowing it might be available cheaper elsewhere)? Depends on the person.