Being told that a doctor won’t do a test because it’s not worth it has a psychological cost that is higher than being told that the screening test came back positive and they need to run some more tests.
You are incorrectly calculating the “value of the appointment” from precisely the wrong viewpoint. Remember that healthcare is about the patient’s health, not the bill.
No, you're missing the point. Over treatment is a serious problem in healthcare. There is always some risk of iatrogenic harm, and for many tests the risks outweigh the benefits. Many tests don't even have a simple positive or negative result: often the outcome is inconclusive.
You are incorrectly calculating the “value of the appointment” from precisely the wrong viewpoint. Remember that healthcare is about the patient’s health, not the bill.