Is the problem not so much the testing, but that most current treatments for cancers are so crude? If you have a relatively asymptomatic cancer, the treatments (chemo, surgery, proton beams) and psychological stress of discovery could be worse (statistically) than letting the body naturally take care of it. This probably depends very much on the cancer ( e.g., some Thyroid cancers might be better left alone).

If our best treatment for fixing a harddrive was to hit it with a hammer, then maybe we'd also conclude monitoring for minor bit errors in data centers is unwise too.

Fair point: if we had a completely non-invasive cancer treatment then that would be a game changer (I made that some point in an earlier comment far down in the thread). And in that case it would lead to improved patient outcomes. But the current regime of tests+treatment options does not in the general case - and there are quite a few exceptions that mostly have to do with genetics - lead to improved outcomes.