To compensate for this disadvantage to the buyer, are supposed to prevent news of the order causing a price change at the other exchanges by spreading faster than filling of the order,
This is simply incorrect. There is a regulation which requires exchanges to transmit news of price changes to the other exchanges as rapidly as possible. The purpose is to ensure that all fills happen at the NBBO.
In concrete terms, if BATS has a BUY@$20.00 and ARCA has a BUY@$20.01, BATS is forbidden from filling your order.