Going forward into the future and not measuring more accurately because we are worried about false positives in our current limited understanding is a very conservative take.
On what basis do you say this? There is an extensive literature that refutes this. Scanners have been getting much better since the first CT scans and many more people are getting them.
Um, that's still a tumor.
I mean, with that much data, you may be able to understand under what timeframe a tumor is actually of concern. What's so bad about having some false positives?
Having invasive surgery. Undergoing chemotherapy. The former is bad, the latter is basically a 'lets hope it kills the cancer before it kills you' situation.
It's arguable which one is worse, but I'd rather not have to ever partake in either of them again.
I think this is currently seen as too expensive to do for people who have lower risk, but I mention it as an example of something that one could check for more routinely given much cheaper ultrasound scans.
Prophylactic ultrasound exams are also apparently much more plausible on medical cost/benefit than prophylactic CT exams, because the CT exams very slightly increase one's cancer risk (https://xkcd.com/radiation/), where ultrasound doesn't.
(At a friend's doctor's suggestion, I started taking alkali citrate supplements and switched from almond milk to oat milk; I now apparently rarely get kidney stones.)