Interesting discussion here. I completely agree with Edward. HFT just serves the brokers and trading houses. For real investors it is not important that their trade executes within seconds. They could wait for the end of a round (i.e. until a new blockchain block is found), which will match all trades. This will give all real investors an effective spread of 0. This will serve the businesses and investors and not some parasites in between.
But, after clearing all the orders possible using that approach, the residue, the trades that cannot happen at that "fair price", do still exhibit a bid/ask spread presumably.
This wouldn't be a spread. They just placed orders which nobody wants to fill.
If AAPL is worth 500 USD and I place an order at NYSE to buy AAPL for 450 USD, then the order is not filled. Would you then say that the spread is 50 USD, just because there is no counter party??
With regards to the point you making about costs. Spreads have come way down in the last 10-20 years due to computers. I mean the whole point is that computers are more efficient than people in some regard. The bandwith HF trader is really not that much compare to the volume they trade. And they pay for the bandwith.
As said, the spread would be zero in a round based system. All this talk, about the benefits of HFT is just a baseless rumor that is spread by large banks, because it is a way for them to make money.
If you are talking about the efficiency of computer trading you should distinguish between computer algorithms that detect bubbles and predict prices (which is a good thing) and HFT (parasites).