the primary reason is "the rule of law" in our western democracies.
meaning that the citizens devolve upon the State the functions of peacekeeping and administering justice, and that essential rights and duties are laid down in law. If you were to stand the argument on its head, and ask what would happen if people were free to administer justice themselves, then you see why due process is so important. Arbitrary arrest and indefinite imprisonment without charge or trial, use of excessive physical force and intimidation, torture, using prisoners as gratification through violence and abuse, unfair trails, mistaken identity, lack of evidence.. need i go on?
one of the most basic principles in jurisprudence is "habeas corpus" latin for "have you the body?" meaning, has a crime actually been committed? without this essential principle, you open the floodgates to anarchy and brutalism. Otherwise you'd be arresting people simply because you didn't like them, not because they'd done anything.
I think you'll find Ed will have something quite insightful to say on this subject