Most of the "Arrests" have been done on people that might have become citizens if given the chance. The rest are the undesirables that will NEVER be able to pass the muster. One of easiest ways to deport a person and they won't come back a quickly is to get them into an immigration court and make a ruling one way or another. Those that pass may be able to begin the long journey to getting citizenship. Those that don't can be easily dealt with by Homeland and either be deported right then or, if it's serious, lock their tired butts up.
You may be right. Maybe we shouldn't spend all that money on judges, prosecutors or public defenders. But the law doesn't read "Citizens only" it reads "Persons". If we resort to the method of just saying they are guilty and then deporting them or imprisoning them then what's to stop every law enforcement officer from just determining you are guilt and sending you to prison.