Would they start noticing large increases in cancer rates traditionally only found in the elderly, suddenly being found in younger and younger populations? Or a massive decrease in, say, fertility rates?

Lol. You have a lot more hope in humanity than I do. I think that anyone who brought such a scheme to light would be silenced by social pressures.

I don't know much about the politics of science, but I imagine that the individuals who actually did bring such a scheme to light would become a pariah in the community, and they are smart enough to realize it. Most people just go along to get along, they aren't going to take the risk that they're wrong and be known as the crazy conspiracy theorist for the rest of their career.

But maybe you're right. I suppose it depends on whether you think society values truth more than popularity. Many people fear social rejection more than death, sometimes even seeking death as a solution to social rejection... If the social pressure says "keep your mouth shut, and don't question xyz" the extreme majority will not question it and even go out of their way to shut down others who do.

Why?

Because fitting in is human nature.

When our ancestors saw the rest of the tribe running from something, the ones who stayed behind to see whether running was the right decision or not were removed from the gene pool.