> antithetical to the goal of promoting sound science
That's perhaps an argument for the sciences directly built on positivism (the philosophical positivism), but that list ends quickly. Everything else is based on at the very least odds, but mostly consensus, and convincing based on those is required for anything beyond a few basic sciences.
And positivism only covers math, large parts of physics and chemistry (but not all), and ... that's mostly it. I mean, you could argue small portions of economics, biology also qualify, but only small portions.
Consensus itself, like presented in climate science and medicine, is an argument by authority. So if you convince someone of the truth of, say, global warming, you have in fact convinced them mostly of a social fact: that lots of people studying this problem seriously come to this conclusion. You have not convinced them that "because X leads to Y, here's the proof, Y leads to Z, here's the proof, this will now happen". You can't do that. These sciences don't work like that.
Things like climate science, medicine, psychology itself, ... just aren't made up of rational argument but from tying anecdotes into a larger framework and some amount of statistical inference. For all those sciences any positivist would say that
1) there are (very small) odds that the science is entirely wrong
2) the odds that significant parts or specific studies, even when executed entirely correctly and with integrity, is quit large: obviously 1 in 20 should be outright wrong at 95% confidence