I agree that most labs are probably not out to defraud people. But without replication I don't think it's reasonable to have much confidence in what is published.
This way papers are peer replicated in an emerging manner because the knowledge is passed from one group to another and they use parts of that knowledge to then apply it to their own research. You have to see this from a more holistic picture. Individual papers don't mean too much, it's their overlap that generates scientific consesus.
In contrast, requiring some random reviewer to instead replicate my full paper would be an impossible task. He/she would not have the required equipment (because there's only 2 lab setups in the whole world with the necessary equipment), he/she would probably not have the required knowledge (because mine and his research only partially overlap - e.g. we're researching the same materials but I use angle-resolved photoemission experiments and he's doing electronic transport) and he/she would need to spend weeks first adapting the growth recipee to the point where his sample quality is the same as mine.
AFAICT meta-studies is the level where we as a society really can try to say something intelligent about how stuff works. If an important question is not included in a meta-study, we (i.e. universities and research labs) probably need to do more research on that topic before we really can say that much about it.
But publication is not a closed system. The "published, peer-reviewed paper" is frequently an artifact used to decide practical policy matters in many institutions both public and private. To the extent that Science (as an institution in its own right) wants to influence policy, that influence needs to be grounded in reproducible results.
Also, I would not be surprised if stronger emphasis on reproducibility improved the quality of conversation among scientists.
I never seen papers as "truth", but more as "possibilities". After many other "proofs" (products, papers, demos, etc.) you can assign some concepts/ideas the label "truth" but one/two papers from the same group is definitely not enough.
Implicit in this process is that the authors are acting in good faith. To treat the authors as hostile is both demoralizing for the reviewers (who wants to be that cynical about their field) and would require extensive verification of each statement well beyond what is required to return the review in a timely manner.
Unless your paper has mathematical theory (and mistakes do slip through), a publication should not be taken as proof of something on its own, but a data point. Over time and with enough data points, a field builds evidence to turn a hypothesis into a scientific theory.