They can decide the outcome of a battle; I've read it many times in reports – unexpectedly finding a Utopia in the very corner, and then everything changes magically.
They might decide, or they might not. It's unlikely you'll find a Utopia in the corner. Would you start running off into the unknown, hoping for the best, if there's no guarantee of finding what you're looking for? Most likely, you'll find nothing there and waste your auto-move.
The Auto-move feature tempts players to "cheat."
That's a completely different question; many things can tempt players to cheat. Anyone can cheat if they want to.
