Let me take a step back here, because despite the fact that it sounds like we're arguing, I find myself in total agreement with other comments of yours in this thread, in particular your description of how trials should work; I could scarcely have said it better myself.
Here's what I claim: the rules of evidence constitute crude attempts to impose some degree of rationality on jurors and prosecutors who are otherwise not particularly inclined to be rational. These hacks are not always successful, and occasionally even backfire; and they would not be necessary or useful for Bayesian juries who could be counted on to evaluate evidence properly. However, removing such rules without improving the rationality of jurors would be a disaster.
(Let's not forget, after all, that there were people here on LW who reacted with indignation at my dismissal of certain discredited evidence in the Knox case, protesting that legal rules of admissibility don't apply to Bayesian calculations -- as if I had been trying to pass off some kind of legal loophole as a Bayesian argument. Such people were apparently taking it for granted that this evidence was significant, which suggests to me that it is very difficult for people -- even aspiring rationalists -- to discount information they come across. This provides support for the necessity of rules that exclude certain kinds of information from courtrooms, given the population currently doing the judging.)
Okay, then I think we're in agreement. I guess I had interpreted your earlier comment as a much stronger claim about the mapping between pure Bayesianism and existing legal systems, but I definitely agree with what you've said here. I would just note that it would probably be more accurate to say that the rules of evidence are hacks to approximate Bayes and correct for predictable cognitive biases, though perhaps in this context those aren't quite separate categories.
In 2004, The United States government executed Cameron Todd Willingham via lethal injection for the crime of murdering his young children by setting fire to his house.
In 2009, David Grann wrote an extended examination of the evidence in the Willingham case for The New Yorker, which has called into question Willingham's guilt. One of the prosecutors in the Willingham case, John Jackson, wrote a response summarizing the evidence from his current perspective. I am not summarizing the evidence here so as to not give the impression of selectively choosing the evidence.
A prior probability estimate for Willingham's guilt (certainly not a close to optimal prior probability) is the probability that a fire resulting in the fatalities of children was intentionally set. The US Fire Administration puts this probability at 13%. The prior probability could be made more accurate by breaking down that 13% of intentionally set fires into different demographic sets, or looking at correlations with other things such as life insurance data.
My question for Less Wrong: Just how innocent is Cameron Todd Willingham? Intuitively, it seems to me that the evidence for Willingham's innocence is of higher magnitude than the evidence for Amanda Knox's innocence. But the prior probability of Willingham being guilty given his children died in a fire in his home is higher than the probability that Amanda Knox committed murder given that a murder occurred in Knox's house.
Challenge question: What does an idealized form of Bayesian Justice look like? I suspect as a start that it would result in a smaller percentage of defendants being found guilty at trial. This article has some examples of the failures to apply Bayesian statistics in existing justice systems.