Depends. I would like to think that "the public" would notice all those silly cancer patients showing up to clinic (don't they know that cancer is cured twice a week at every major hype factory, err, university?) but, no.

Pie in the sky it is, then! If only a field existed that attempted to quantify the expected variation from a given size and design of experiment.

That field would be of great use to major nation states. So much so, you might call it statistics. The practitioners would probably be big party poopers, always referring to weird concepts like "regression to the mean", "power", "effect size" and other unexciting yet critical details. I imagine there would be funny videos on YouTube about these people, and "real" researchers would happily ignore them while they jerk each other off in P01 study sections.

Anyways, let's keep science the way it is. There's no way the process or its results could possibly be improved!