If you do a screening and find something that might be cancer and do nothing about it, you've committed a major ethical violation. If you tell the patient "we found something that might be cancer but we suggest you don't do anything about it so we can get more data on whether it ends up killing you", well, the patient will probably see another doctor.

I'm not sure how this would work. Doctors start ordering lots of MRIs that wouldn't have been ordered before, and some percentage of those that wouldn't have been ordered before show tumors. Now what to do you do? If you are just doing it to gather data, you don't tell the patients the results, I guess? This seems unethical.

If you do disclose the results and proceed with a normal patient relationship, you are in the same dilemma as above. You don't know if the tumor is dangerous or not, so the safe course is to do a biopsy, which is itself often invasive. Depending on the results that may lead larger surgeries to exicse large parts of organs and/or the starting of chemotherapy.

Also MRIs are expensive, and in the U.S. a significant amount of that cost (usually hundreds of dollars) is borne by the patient, even if they are insured.

But I don't think we lack for MRI or CT data, there are lots ordered every year. The biggest problem with gathering your data set would be medical privacy regulations. I would guess that medical researchers have already tried longitudinal studies on this to see if different imaging characteristics lead to different outcomes. It's a hard problem, the only data you really get from scans is tissue density, which can probably never tell you what you need to know.