Random split exchanges have been tried and are equally gamed. If your random split is based on order count companies stuff orders to gain an advantage. If it is based on qty its a pro rata market which are common.

Having windowed auctions is also common. They are still latency sensitive as the entry/exit information is still subject to races.

Budesh has a good paper outlining batch auctions and their advantages but it still doesn't account for the fact that cross exchange arb is still an issue.