Hoped to find such a comment here, this is basically about mechanism design - how can we design an exchange that removes the additional profits such microscopically low latency generates, when the low latency itself isn't providing value, i.e. the low latency => profit phenomenon is an artifact of the rules of the exchange.
I appreciate your thoughts, but regarding your suggestion: random isn't well-defined. It can be random as in "randomly pick a participant, let it buy/sell as much of the stock as it asked, then pick another participant etc.". This encourages Sybil attacks - participants have an incentive to create other identities for themselves, and hope one of the identities will be picked "randomly". Another definition of "random" may be "randomly pick an order to buy/sell a single stock, execute it, repeat-until". This, I was told on an earlier HN thread, strongly encourages placing more orders than one wants, again in the hope of fooling the "random" part of the exchange. I was told this is actually what's happening currently in exchanges built this way.
I had a suggestion I tried to analyze (even as a possible idea for a mechanism design paper): What happens if "random" is defined as "your chance of getting picked (to be able to sell the stock) is proportional to the amount of this stock you own"? At least, we got rid of the incentive for Sybil attacks (and didn't create the opposite incentive, for conglomerates - separate entities don't have an incentive to present themselves as a single entity, then do the bookkeeping internally). But it's unclear what to do when there are more willing buyers than sellers. Any thoughts, anyone?
I have also wondered whether this whole thing is an artifact of quantization - what would happen if the price granularity was allowed to be as small as one wants?
(In case anyone's wondering, a friend I consulted told me this probably wouldn't fly as a paper - useful economic policy if I can solve that "more buyers" problem, but nothing scientifically novel).
p.s. Sorry for the long comment.