The one mile distance gives the sannin enough time to call their summons and activate their specific modes like Sage Mode and Byakugo. Jiraiya then get's Gamarinsho prepared. As soon as Kakashi, Gaara, and Sasuke arrive to the fighting distance, they hear the song of the toads and they all lose. If for some reason the don't do this, then one use of Kamui and two uses of Amaterasu ends the fight.