Arbitrage is certainly important, and it should happen on a time scale that is faster than ordinary economic events, because markets need some time to adjust . But it is fairly obvious that there are strongly diminishing returns for society as arbitrage becomes faster. Imagine a hypothetical alternative market which operates on a one minute heartbeat, for example: the market algorithm simply runs a secret auction once per minute at a pre-determined time, with bid prices as fine-grained as one millionth of a cent to avoid some pathologies. My hypothesis is that such a market would be as inconsistency- and arbitrage-free as what we have today, to an accuracy where the difference simply doesn't matter to ordinary investors - where by ordinary investors, I mean actors with an investment horizon that is measured at least in months. So you would have the same benefit to the society while using less resources (resources that are currently used to get ping times down etc.).
At the same time, look at your last argument: HFT traders are basically competing among themselves, but since their response times have to be so fast these days, they are mostly competing to exploit each other's weaknesses and the weaknesses of the trading algorithms of larger investment funds.
In the hypothetical market, competition between algorithmic traders would still happen. But since there is now more time for computation, the emphasis shifts away from hacking to get short response time and instead towards making more intelligent decisions about price. There might be a shift towards more emphasis on evaluating fundamentals, and that can only be a good thing for the efficient allocation of capital.
 Incidentally, I suspect that the reason that much of what neoclassicals say about the macroeconomy is wrong precisely because they incorrectly assume fast arbitrage in macroeconomic events.