You might be right in an ideal world, but in reality there are significant resource constraints on healthcare.

What would be more likely to happen in that scenario, is that so many people would be seeking care that the 5% who were positive would be unlikely to even get the care they need.

Further, such an influx would have knock-on effects on unrelated patients, whose care would suffer due to the severe lack of resources.

This is all magnified if the resource is not a general practice physician, but a specialist.