Can you tell us what you mean technically by "privileged" access? Is there a threshold in dollars you have in mind for what is an acceptable fee for connectivity, or is it something else?

Is it a matter of the stock exchanges profiting from this, or the fact that it's possible at all?

I can't see how it can ever be possible to give everyone the same information at the same time. Latency will always be there, and renting rack space in a building near to the exchange will allow the information to reach you before the opposite coast of the country. Although this might mean that the owner of the neighboring building is the one making money, and not the stock exchange itself.