It's not that the public doesn't trust the abilities of scientists.
It's that they don't trust their motives. We have a long literary tradition that meditates on scientists that "only cared about whether they could, not whether they should," and the politicization of sciences makes people wonder not whether scientists are incompetent, but whether they have "an agenda," i.e. whether scientists are basically lying through their teeth and/or pursuing their own political agendas in the interest of their own gain, rather than the public's.
At that point, it's not that the public thinks "If I argue loudly enough, I can change nature," but rather "I don't understand what this scientist does, and I'm sure he/she is smart, but I don't believe they're telling me about nature; rather, they're using their smarts to pull the wool over my eyes about nature and profit/benefit somehow."
So the public isn't trying to bend the laws of nature through discourse, but rather simply doesn't believe the people that are telling them about the laws of nature, because they suspect those people as not acting in good faith.
That's where a kinder, warmer scientific community comes in. R1 academics with million-dollar grants may sneer at someone like Alan Alda on Scientific American Frontiers, but that sneering is counterproductive; the public won't understand (and doesn't want to) the rigorous, nuanced state of the research on most topics. It will have to be given to them in simplified form; Alan Alda and others in that space did so, and the scientific community needs to support (more of) that, rather than sneer at it.
The sneering just reinforces the public notion that "this guy may be smarter than me, but he also thinks he's better and more deserving than me, so I can't trust that what he's telling me is really what he thinks/knows, rather than what he needs to tell me in order to get my stuff and/or come out on top in society, deserving or not."