>Let's say a murder conviction is based on 37 different security recordings clearly showing the defendant murdering the victim. The recordings make it a certainty that the defendant is guilty.
This is the problem with this approach. Let's say the guilty party is someone who looks like the defendant. Now it doesn't matter how many security cameras there are, they all record what happened: Someone who looks like the defendant commits a murder on camera. The number of recordings doesn't inherently show whether it was the defendant or a double.
Or let's suppose that the evidence has been fabricated by someone trying to frame the defendant. Someone who fabricates one recording to the satisfaction of the jury can generally fabricate 37.
Or perhaps it was the defendant on the video but it wasn't a murder, it was a staged public death in cooperation with the alleged victim who subsequently went into hiding.
All of these things are individually relatively unlikely, but they don't become any more unlikely as a result of additional recordings.
This is one of the reasons why conviction rates are generally so high. Suppose (picking a number out of a hat, since we can't really know) that 60% of the accused who go to trial are actually guilty as a factual matter. But of the ones who aren't guilty, 0.6% are because a double committed the crime, 0.5% are cases where the defendant is being framed by a third party or the police, 0.7% are cases where the defendant could show a lack of guilt but doing so would endanger someone else and the defendant prefers to risk prison over endangering that person, etc., and when you add up all the individually low probabilities it turns out that at least one of them has happened in a quite substantial percentage of cases.
The trouble is that the defendant who goes to trial and claims to have been framed is not believed, because only 0.5% of cases are genuine instances of framed defendants (and juries intuitively understand that), and the prosecutor is too often allowed to infer from this that the remaining 99.5% of defendants are actually guilty, rather than that some quite large percentage of them are not guilty but for some other reasons, each of which seems about equally unlikely in any given case and is thus subject to the same misleading inference. But the alternative, to rigorously consider each of the individually not very likely alternatives, is extraordinarily expensive -- which is why statistics is given the short shrift.
At the end of the day the problem is that proving guilt to a level of certainty that would satisfy us if we were being rigorous about it would also cost too much and be too difficult for prosecutors to prove in most cases to satisfy our political desire to incarcerate "bad people" on a mass scale without breaking the bank any more than we already do. Rigorous, large scale, feasible budget. Pick two.