My experience is that they go the other way. They are reluctant to prescribe them because they are hoping that it is a virus and they often try to not prescribe a second round when the first round failed to clear the infection up. Often because the delay allow the infection to settle in nice and deep.
Either way this test could be quite useful.
Wow. You have the opposite doctors of what I have seen. They will prescribe antibiotics for viral infections. There are even studies that urgent care doctors do that even more. This tendency is why we have so much antibiotic resistance.