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.