Everybody would see the arbitrage within the next trading cycle. So, rather than try to eliminate the arbitrage opportunity, put reaction times into a human time scale and let every actor share.
Tie breaks can be fair split with cryptographically random split for the last share, for example.
Yes, "all or nothing" would complicate, of it's still a necessity, but all those things are solvable, if we believe in fairness of markets and avoiding the next flash crash.
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.
Tie breaks can be fair split with cryptographically random split for the last share, for example.
Yes, "all or nothing" would complicate, of it's still a necessity, but all those things are solvable, if we believe in fairness of markets and avoiding the next flash crash.