I heard the same argument from my doctor when I wanted a blood scan.
But what's the intention? If you do a scan and then try to find everything that is wrong about you, you're 100% right, there will be false positives and unnecessary panic/medication etc.
However if you just collect data for months and years and WHEN you get a symptom you have a lot more data then we should be able to give better diagnosis faster. If we do that for long enough as humanity and there is data sharing the accuracy of the whole thing will increase a lot.
I think it's (at least partly) about the psychological impact of finding something unusual. Even if you know that it's probably nothing and understand the Bayes theorem, there will be a "what if" that might be strong enough to do actual harm (nocebo effect).
Compare: The placebo effect works (at a reduced rate) even if you tell people they're getting a placebo!
This. All diagnoses are "given this set of symptoms and test results, which is the most likely issue".
By having a whole slew of test results already, you will have much better priors.