Except that the medical system already does that for various types of common cancer screening such as breast cancer. It is frequently detected extremely early when it is medically insignificant and patients may be recommended to just wait and watch with more frequent screening. Increased vigilance would have been impossible without early detection and early detection for breast cancer is viewed very positively and is very positive for society.

We have a system that partially results in anxiety because cancer screening is frequently only done when cancer would already be medically significant. A positive result usually means medically significant cancer because as a society we already chose to not screen when it would be medically insignificant. This is perfectly reasonable if the test is expensive, inaccurate, or harmful as even just the harms from doing the test in bulk could result in societally worse outcomes than occasional early detection. However, the rise in "medically unnecessary" screening indicates that we have turned the corner on that in many cases; that or it is easily billed corruption which is a separate problem.