The problem is that laypeople or bureaucrats can't judge highly specialized technical contributions. It's already difficult to do if your subfield is a different niche.
It's not that difficult, at least in science and science-adjacent fields. The scientific method still follows the same principles.
If you are used to reading papers, you can tell when someone has elided important detail, or not included the evidence for their claims - or, if someone [or a whole subfield] is using technical language to obfuscate their work.
I don't claim that paper reviews have to be or can be perfect - only that they could be held to a better standard than they are now.
We see plenty of avenues for publishing to a worse standard (self-publishing on an internet aggregator, for example). Let's see some avenues for a better standard.
Why isn't this a science in itself? We could trial some different standards and statistically compare them.
[It was not my claim that scientific papers must be understandable by laypeople, although I think this is an ideal case. If not, it should at least be understandable by people in an adjacent subfield - otherwise, it's just a small group of people talking amongst themselves]
“the scientific method” is rather loosely defined and wide.
What passes as “the scientific method” in some fields would not in others.