Because modalities like MRI are non-ionizing and therefore not intrinsically harmful, I think it is reasonable to consider a wild extreme: in some future, what if a large group of people underwent imaging every month or every year. It's possible to imagine gaining a very good understanding of which lesions have malignant potential and which ones don't.

The transition period that we are in now - where we are gaining information but not yet sure how to act on all of it - is painful. There are a lot of presumably unnecessary follow-up procedures. But it's possible that at some future point, we'll understand that 0.8mm nodules come and go throughout a lifetime and don't merit any action, whereas {some specific nodule in some specific location} almost always progresses to disease.

Obviously what I'm describing is research, and so I'm not saying that we should treat clinical protocols differently right now. But I think it's not too hard to imagine that we can get to a point where we have a very good idea about which lesions to follow/treat and which lesions to leave be.

Why would we not want to know about a tumor in the body? I assume competent doctors will assess the risk of such a thing, but knowing about it is better than not.

Doctors will optimize for patient outcomes, usually by doing all they can. Sometimes, this doesn't scale well. For example, the US Preventative Services Task Force stopped recommending routine PSA screening among asymptomatic patients to detect prostate cancer in 2012. They based their decision on a careful review of medical research, noting the screening didn't have much of an effect on mortality but could cause stress or invasive follow-up tests. Urologists generally opposed the decision. The USPSTF has since walked it back to, "Talk about the risks and benefits." I've looked at survey results for my state, and the numbers indicate a good proportion of men are told the benefits of a PSA but not any risks

Patients are even less reasonable. If you tell somebody they have a tumor, they will now have a constant stress. If you say "cancer," they'll likely undergo expensive and potentially harmful treatment, even if "watch and wait" was a totally valid choice (e.g., slow-developing prostate cancer for very old men). Remember how Angelina Jolie had a double mastectomy after being told she had a good chance of developing breast cancer? That behavior will lead to a lot of unnecessary pain, debt, and lower-quality lives if it became normal.

It'd be hard if not impossible to ask doctors don't share knowledge about a tumor with patients. But in some cases we intentionally ask them not to go looking for tumors because the expected value of a positive result is a negative impact.

Everyone gets cancer eventually, it's inevitable if you live long enough. There's no point in knowing that a small, slow growing tumor will kill you in 10 years if a heart attack is going to kill you in 5 years anyway. Knowing about the tumor just creates more psychological stress and potentially extra unnecessary medical treatments for no benefit.