(I'm using an uncomfortable and illustrative example, but a colonoscopy is honestly pretty safe and boring as invasive clinical diagnostic procedures go)
However I think this concern would be reduced if we had better first-line screening like the tests in TFA; the harms come from using a relatively-risky assay like colonoscopy for regular screening in healthy individuals, whereas if we had better noninvasive screening, the colonoscopy could be reserved for patients where there's a higher probability of a positive diagnosis.
[1]: https://jamanetwork.com/journals/jama/fullarticle/2529486
For the USA...
Something around 1.8 million people are diagnosed with cancer per year. At a 50% false negative rate, all else being equal it would detect 900k of those.
And all else being equal, at a 0.5% false positive rate, if it were used as suggested it would incorrectly diagnose cancer in around 1.6 million of the population.
So around 60% of the people it says has cancer wouldn't have cancer. I guess it depends upon what you mean by "somewhat reliable".
Medical tests are complicated. They often have significant false positive and false negative rates. Testing people at scale increases the number of people with wrong test results and can cause harm if you start treating people based on wrong test results. The more healthy people you test the more false positives you get.
The goal of evidence based medicine is to use tests when they can help. It's not to test as many people as possible. This is reasonable. You want to improve patient's lives. Whether or not a test is improving patient's lives is often not easy to answer and has to consider many things.