Also, just to answer your actual hypothetical of "testing" the criminal justice system:
I'm not sure how you would test it. You can run a "mock" trial, although I'm not sure it's so easy - to be realistic, I think you need to create a scenario which can plausibly go in either direction (innocent or guilty). But what would that tell you? I mean, "beyond a reasonable doubt" is a pretty high standard and all, but if you make it seem pretty clear that someone is guilty when they're "really" innocent, that doesn't mean much, because this is fiction - you made up a tricky case, and people got it wrong. So what? The question is how often does real life cause a tricky scenario to manifest.
You can go the other way and set up a situation that's pretty clear, but I'm not sure that will be very insightful.
That's not to say we can't think of some way to test the system which does work - I'm sure smarter and more knowledgeable people than me can think of something. But that brings us to problem number 2 - now what? Let's say people got it wrong. What do you do? It's not like you can just change the way trials work - you need laws for that.
The most you can reasonably do is use trial tests as a basis for potentially changing the law, but that's before any politics gets involved. Realistically, I'm not sure you can do much more than gets done now - once in a while an article gets written about a specific bad practice, it causes a public stir, and the law maybe gets changed. I'm not sure systematizing any of the testing steps really changes anything else in this picture.
And we might as well ask about easier things, why don't we test them. I.e. why not test economic policies by building "test cities" which have different economic policies, and seeing which ones work? The States kind-of does this with different laws in different States. So there is kind of a natural experiment of the effect of different laws on economics, on justice, etc. This does affect some things, but I'm not sure the effect is very large (but then again, I'm not an American, so I'm not that up to date on the politics there. It's certainly an idea that a lot of lip-service is paid to, but maybe it's more than that).