The ONLY reason HFT companies invest money to shave milliseconds is to have quicker access to orders that come into the system (this article elaborates: http://blogs.wsj.com/marketbeat/2012/09/20/collocation-the-r...)

It absolutely has nothing to do with reacting to real-world events. So if all activity were to take place at 1 second intervals (kind of like microprocessor clock) - their main advantage would go away.

That only matters because both exchanges have the same problem. I think it is definitely true that if both exchanges ran on a synchronized 1 second schedule the advantage would go away, because the information from the previous round would be uniformly available early in the next.

It is less clear to me whether fixing just one exchange fixes both or neither.