The regulator cares about more than just the mean price. The idea behind Reg NMS is that anyone who places an order at a protected venue should get the best price available, not just something close. It isn't enough for the differences to just average out, because some people get poor execution in one direction, and others get poor execution in the other.

Agree but consider this:

If the timing is perfectly tractable the system is gamed. A small amount of noise that prevents manipulation is a good thing over time for the market. It means the stock is going to have less vol which increases the value of the market equity given constant cash flows. That's another policy goal more broadly. That is, if it works this way.