It's a human factors thing. If two patients both have a cancerous tumor that does not need treatment, the patient that did not have a screening is better off. The patient who was screened will deal with anxiety from having a positive screening result in addition to any negative effects from the screening and follow ups. Many patients are not comfortable living with a detected tumor, even if the standard of care is to watch and wait. Of course, the opposite scenario is also true --- if both patients have a tumor were removal would be best, the one that gets screened has a better outcome.

Maybe if we were all pretty rational people, we could better manage positive screening results and follow up actions that lead towards taking no specific action; but that's not where people are at the moment.

There's a tradeoff of early detection of fast growing tumors that are likely to cause issues vs detection of slow growing tumors that are likely to not cause issues except if they're detected. You can see how the consensus is shifting on things like breast, prostate, and colon cancer screenings over time. My TLDR is that we developed tools and methods, started applying them and have generally reduced the screening frequency over time as we understand more about the tradeoffs.

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.