" But adding an extra decision point where the worst that can happen is that the prosecution that was going forward keeps going forward, and the best that can happen is that the case gets dropped without the ordeal of a trial sounds like a substantial improvement even if it doesn't always work."

Uh, that's not the worst that can happen. The worst that can happen is that those who actually committed crimes are let off because they learned how to 'beat' a polygraph, or who just got plain lucky. And if you know already that your suspect is innocent, then why the polygraph?

Look I understand how adding some voodoo scapegoat to a complicated social construct can be used to change institutional mores that are impenetrable otherwise. So in that sense, I have no rational reason to discourage the use of a polygraph here; just like one can say 'if homeopathy helps people, why shouldn't they use it? And why shouldn't we finance it from the same means we finance regular health care?'. From a utilitarian point of view, there is no denying this. I maintain that it's still bad (maybe not a net negative, but a negative still) to use acknowledge superstition this way.

If a polygraph is a filter that just doesn't work, then it's a total waste of time as it won't work as a filter, or anything else for that matter.