Anecdotal evidence is the bases of witchcraft, homeopathy and a host of other confused dogmas. They're built on taking one coincidence and creating a castle of speculation, all the while thinking "I have figured out something those scientists have missed!"
It takes a host of data to create information. On spec of data is largely useless for illuminating any complex subject.
You want people to believe in global warming, coronavirus, and healthy foods, make global warming, coronavirus, and healthy food test kits. I hate to burst your bubble, but when the rubber hits the road, science journals are just text on paper, disconnected from reality. Gravity, radiation, magnetism, etc were discovered through experimentation and demonstrations. We live in a dark age of irreproducibility.
Take health industry and cybersecurity industry for example. The former publishes controversial results every weekend, and the latter has us trust closed source systems due to appeal to authority.
Anecdotal data isn't much but it's your data, and that sure is better than wrong data.
At least for complex subjects like health, weather etc. "I saw a snowflake! Global warming has to be wrong!" is not any kind of conclusion.
No, I can look at and trace the proofs in any mathematical publication. I can look at and trace any open source code. If something works, I should be able to test it. And it's your flaw to assume people will play along with the onus.