A few comments:
It is somewhat confusing (at least to legal readers) that you use legal terms in non-standard ways. Conflating confrontation with hearsay issues is confusing because making people available for cross-examination solves the confrontation problem but not always the hearsay one.
I like your emphasis on the filtering function of evidentiary rules. Keep in mind, however, that these rules have little effect in bench trials (which are more common than jury trials in state courts of general jurisdiction). And relatively few cases reach trial at all; more are disposed of by pretrial motions or by settlements. (For some data, you could check out this paper by Marc Galanter.) So this filtering process is only rarely applied in real-world cases!
Before suggesting that we should exclude evidence of low reliability, you should probably take more time to think about substitution effects. If lawyers cannot use multiply embedded hearsay, what will juries hear instead? Also, you would want to establish that juries would systematically err in their use of such evidence. It is not a problem to have unreliable evidence come in if juries in fact recognize its unreliability.
I’ve recently spent some time thinking about how we might apply the scientific method towards designing better rules of legal procedure and evidence. It turns out to be trickier than you might think, largely because it is hard to measure the impact of legal rules on the accuracy of case resolutions. If you are curious about such things (and with apologies for blatant self promotion), you might want to read some of what I wrote here, particularly parts 2-4.
That critique might sound good in theory, but I think it falls flat in practice. Hearsay is a rule with more than 30 exceptions, many of which seem quite technical and arbitrary. But I have seen no evidence that the public views legal systems that employ this sort of convoluted hearsay regime as less legitimate than legal systems that take a more naturalistic, Benthamite approach.
In practice, even laypeople who are participating in trials don’t really see the doctrine that lies beneath the surface of evidentiary rulings, so I doubt they form their judgments of the system’s legitimacy based on such details.