Wrt the issue at hand: yes the cancer was found as an incidental finding on a scan performed for another indication (shoulder pain) -> the question remains whether your father benefitted from finding the cancer. This is seldomly the case.
Anecdotally, everything is possible but on a population scale, actual survival benefit is rare - whereas suffering from the downsides is not - even if only counting unnecessary healthcare cost and time wasted.
I agree anecdotes don’t generalize and broad population screening sounds like a bad tradeoff. What I’m wondering about instead is risk-stratified situations: once someone already has elevated risk or prior lung disease and you’re imaging them periodically for legitimate reasons, incidental findings may carry much more signal than noise.
For example, people with prior tuberculosis often get periodic chest X-rays, not to screen the general population, but because their baseline risk is different. My dad had prior lung disease and existing imaging to compare against, which probably made the finding actionable rather than just another false positive.
So not “scan everyone”, more “the usefulness of incidental findings rises quickly once pre-test probability isn’t tiny”.