While I still agree with your main points, it should be pointed out that any process that can be actually executed by real humans will throw up false positives. For that matter, any process actually executable by a benevolent AI will throw up a certain number of false positives, too. We need to be ready to deal with that.
So, both faulty process and the death penalty is the problem.
At that point, it'd probably be more economical to just have the universal nanotechnology modify humans to be unable to commit crimes, indeed, unable to think them.
So, both faulty process and the death penalty is the problem.