That's true. The problem is that most diseases occur in a very small percentage of the population (less than 1/100 or 1/1000), which means that unless the false

That's true. The problem is that most diseases occur in a very small percentage of the population (less than 1/100 or 1/1000), which means that unless the false positive rate is exceedingly small, testing the population as a whole will still produce a bunch of false positives. This is one of the reasons why doctors only order a test if there is a reasonable suspicion that the underlying disease is present.