A Sneaking Suspicion
Why exactly is government divided into three parts? Isn't is possible, for example, to have the domestic police (FBI, DEA) run by a separate branch than a more international (Pentagon and State Dept) branch? I think it is a fine idea to have the prisons run as a separate branch than the police. American prisons were invented by far more religious-minded people than the elected "tough on crime" types.
Now, of course, three is simpler than five. The simplest answer might just be that a unitary power is too easily corrupted, a bi-lobed power is too obviously imbalanced if either side gets a little more power, and three is the next smallest number.
However, I suspect it has more to do with the Trinity.