Research gets cited constantly in public debates and is used for policy decisions, so the public should be able to quickly separate the good from the bad, the "maybe this is true" from the "this is empirically proven."
The public has lost a lot of trust in Science because research papers have been used to push political agendas, which can then never be questioned because doing so means arguing with a supposed peer-reviewed scientific consensus.
Replication and meta-analysis are an important part of this.
Most scientists are in fact very conservative with how they claim their results - less so university PR departments and “study shows” clickbaiters.
Instead I got PIs happy to say that weak evidence "proved" their theory and to try suppress evidence that negatively impacted "fundablity". The most successful scientists I worked with were the ones who always talked like a PR puff piece.
I did theoretical physics (no money) and my experience totally matches what the other person described.
The public has lost trust in science because 10 to 30% of it is scientifically illiterate [1]. (Tens of millions of American adults are literally illiterate [2].)
That's what lets activists and politicians cherrypick bad science that supports their position or cast a scientific consensus as unquestionable.
[1] https://carsey.unh.edu/publication/conspiracy-vs-science-sur...
Obviously reproducing results as part of peer review is not a workable (or even coherent) solution. I don't pretend to have any idea what a solution might be. The obvious issue is that academic publications were never intended as political tools and should not be made into that.
On several occasions I've had interactions with laymen where I found myself thinking "if only you hadn't had access to pubmed and way too much motivation we'd both be better off right now" yet I firmly believe that free and open access to information is a huge net benefit to society on the whole.
It is not, and it cannot be. It is unrealistic to expect a referee working in their free time to confirm studies that often cost millions of dollars. This is a fundamental misunderstanding of what peer review is and why it is useful in popular or heavy vulgarised science.
Politicians, journalists, and university press offices are guilty of this, and they are those abusing peer review to give some studies more weight than they deserve.