I should say, if you know ex ante that certain results are not worth acting on, then when you actually get those results ex post, you should ignore them just the same. So actually running a test cannot formally be the problem.
That is not how medicine works, especially with cancer. Very often we simply don't know whether or not to "ignore" something. But the harms of knowing are not zero, and therefore screening can itself be a net negative. That's why a well powered RCT is required to say whether it benefits patients or not.
We have a more detailed exchange going on elsewhere in this thread, with my latest comment, addressing your more detailed points, here: https://news.ycombinator.com/item?id=27630947
Isn't the only way to learn what things we can ignore and what things we can't ignore to do a lot more testing? Is there a better way to learn that? It seems like having a lot more data from tests is the kind of thing that would have some short term harm but massive long term benefits.