The errors are correlated, not random. Lumps are usually benign cysts. If you start cutting people open for every cyst on a scan, you’d kill a lot more people than you’d save.
This isn’t something you can solve with more scans because the tests test for data that is indistinguishable. They look the same on a scan, there’s an overlap in the assay with some random protein with the same binding sites that is only present in 1% of the population, the coding gene in one person gets repeated in a noncoding region in another, and so on. The “more data” that works is a doctor applying professional judgement (which they’re also famously bad at because biology is a fickle mistress).
More data (daily scans) can mean we get better at medicine, though, and more accurate. You're assuming "daily cancer scans" look just like they do today, rather than eg unobtrusive devices in our daily lives that measure changes over time.
The frequent "muh false positives" comment we hear from doctors appears to be a lack of imagination?
If you're doing non-redundant tests and your uncertainty bars aren't shrinking, it's usually a skill issue.
If it looks like a duck, it might be a duck - or a painting of one. If it looks like a duck, swims like a duck, and quacks like a duck? The joint duck estimation is much more confident now. There might be a few more observational tests one should administer before committing to a duckhood decision, but each tests pins down variables and rejects confounders. Uncertainties are cut down, and we get closer to crossing the threshold between "duck-informative" and "duck-actionable".
Thus, it's often worth it to improve observability. If you managed to make a certain test more reliable, or cheaper to administer, or reduced the chance of adverse effects? Or, in other words, improved SNR, reduced costs, and reduced costs? You can get more information for your buck. Paired with good knowledge: you can make better decisions more easily.
The fact that the thought of "having more information might be bad actually" even occurs in the field of medicine shows just how far it is from being optimal. Having more information isn't always beneficial - some information is genuinely redundant. Some information is not worth the effort of gathering and integrating it. But if you get more information and it results in worse outcomes? You're doing something wrong.