This is actually a big deal in America and a fundamental change in how our government operates. Your idea is right, but since the 1960s judicial authority has grown in a way that increases their responsibility to the point where they're almost legislators themselves.

Because there's a lot of different ways to interpret laws, judges have a fair amount of flexibility in sentencing, and elected judges aren't by default just cronies of whoever appointed them.

I think prosecutors fall under the executive, not the judicial, branch