The first mover could always invalidate the unpublished transaction by sending the coins to himself ? In the worst case, both parties would attempt a double-spend.
Suppose you can send coins to yourself as a free txn.
Bots will constantly place offers, wait for buyers to accept them. When advantageous, they will then send the coins to themselves invalidating the offers. First and second movers are on a level playing field. However, first movers broadcast a large volume of useless txns. This would most likely be a big nuisance for the network. So you could move to a situation where txns require a fee or they get ignored completely.
Suppose you cannot send coins to yourself as a free txn. You need to pay a fee.
Bots will constantly place offers, wait for buyers to accept them. When advantageous, they will then send the coins to themselves invalidating the offers. The threshold will be higher because the advantage will have to be greater than the txn fee. Since second movers back out through inaction, they will be able to back out for free. Again, it sucks to be a first mover and you want to move second.
Backing out needs to have a strictly positive cost. The cost needs to be the same on both sides.