I'm no radiologist but I've seen enough of this done that I'd lean that way. Especially if you consider realistic bounds on time and additional information.
Think about say a diagnostic blood test with a poor sensitivity (but better than chance) on a very rare disease. As an oversimplification: for a bound take your population * workup rate * fatality rate due to workup and you have a baseline needless death due to the screening (NB there is basically always a fatality rate). The number you are comparing to is lives saved due to earlier detection.
Better than chance means it's strictly more information always. But as policy, you shouldn't do it unless you can be extremely confident that lives saves is much larger than lives lost due to the process.
This is a bit counter intuitive, but it is a fundamental issue in a lot of healthcare policy. The real calculations are more complex but in the end it is unavoidably actuarial in nature.
this is not a global optimization problem; it's a local optimization problem. one person is deciding whether or not to spend their own money on an mri, or a blood test or whatever, on themself. they are the ones in the best position to do that, and for very-low-risk tests like mris it is very rare that the optimal decision is for a rich person not to get them
Ignoring the fact that in the real world due to constraints this isn't really a local optimization, if we assume infinite availability you still have a problem that low sensitivity tests lead to excess unnecessary work up risks. Your assertion that it is always easy to get good information leading to correct choices here is just incorrect and probably naive.
The trade offs you are talking about are very well known and have been studied by professionals for decades; none of them will claim it easy - for good reasons.
Note I'm not appealing to authority here. Many people can educate themselves to the degree that in a narrow area of their own healthcare they are as or more knowledgable than the average professional. However, this is not at all easy, and will require a ton of work. The cost benefit for a lot of screening etc. just isn't there; for a particularly symptomatic disease it may well be.
This is actually a bit subtle. For example I've heard more than one radiologist claim that if you look carefully, literally anyone's body scan will contain details that could justify work up.
The fact is, if you do this broadly in a population and you work up everything you see that would justify it, some small number of people will die or suffer serious problems from complications of follow up.
This is a fundamental problem in screening technologies (of any kind) with imperfect sensitivity. You can't get away from this, so you try and be clear that the net benefit is (much) higher.
I'm not even against the idea of baseline scans, but the idea that this part is simple is naive.