A) What do you do when bids and asks do not match up? Who's orders get filled and who's do not? There are several possible answers to this problem, but not are satisfactory.
B) You do not eliminate the advantage of speed because everyone is still incentivized to put in their orders at the last possible moment before the end of the interval.
The world is continuous, not discrete. Therefore, like it or not, trading must be continuous and not discrete.