Did you read my two options? Do you agree option 2 is better than option 1? If so, then scans are better than no scan
You don't need to show that it's possible to avoid false positives. That's doctors being irrational.
You only need to show that it's possible to build a diagnostic system that's better than no testing, and I have shown that already
No. To argue for the benefit of the procedure, you need to show a difference in outcomes. Not that it can detect something, even if it could (which whole-body MRIs clearly don't). That the detection improves your chances of survival.
If you have an growing mass in your body, then if it's cancer, after a year, it might be too late for treatment. Or it may turn out to be nothing: a benign tumor / cyst / fat deposit in an unusual place. Or it may be slow-growing prostate cancer that you can live with for another 20 years, and maybe it's the chemotherapy that will do you in. It's really not that clear-cut in medicine.
To give you have another example: let's say that the risk of appendicitis in people who have an appendix is 1%. And the risk in people who had an appendix removed is 0%. Does this justify proactively removing the appendix? No, because the consequences of complications are much higher than the harm you're preventing. The same applies here: detection, even if 100% accurate, doesn't mean anything. You need to show that what you do with the result actually helps.