The reason you don’t want to do “all of the tests” and “deal with the results” is not about the probability of a false positive, but the consequences of getting one:
“In the United States, estimated deaths per year include: [26][27][28][29]
12,000 due to unnecessary surgery
7,000 due to medication errors in hospitals
20,000 due to other errors in hospitals
80,000 due to nosocomial infections in hospitals
106,000 due to non-error, negative effects of drugs
Based on these figures, iatrogenesis may cause as many as 225,000 deaths per year in the United States”
This is exactly what the doctor parrots back at me. Again, these are outcome statistics for the general population. I'm well aware of these numbers, but I am not an average patient.
I'm not going to look at the outcome of a single test and blindly decide to take a strong medication or to get surgery. If I want a test done, it's because I'm doing research to try and figure out a complicated issue that doctors have not been able to help me with, usually due to their own time and resource constraints. I have all the time in the world, and if a condition is affecting me, I'm going to care more about addressing it correctly than any doctor. I'm completely aware that a test is just one data point, that tests have error rates, and that interventions have risks.
I was one of the first ~1000 to get whooping cough (pertussis) during the 2008 outbreak, before they knew that the vaccine cocktail that my generation was given needed more frequent adult boosters. I figured it out after a few days of digging. Do you want to know how many doctors I had to yell at to finally convince one of them just to run the test? And this is a test with zero intervention risk -- they can't do anything if it comes back positive, they just tell the NIH.
Doctors have gone off the deep end here. Yes, testing has risks, but they should focus on the intervention risks. You should be allowed to run as many tests as you want for informational purposes if you're just trying to figure out what might be going on, especially if you're aware that errors can happen and are capable of acting responsibly with the resulting (single, noisy) data point.
You might have a case if you were paying for the test out of pocket, but I presume you have health insurance. In that case, it is also the doctor's duty to prevent unnecessary spending.
Combined with the fact that most patients are not well informed and will demand pointless or even counterproductive, it is better to leave treatment and testing decisions to doctors, not patients. Even if doctors sometimes get it wrong it is still better than the alternative.
“In the United States, estimated deaths per year include: [26][27][28][29]
12,000 due to unnecessary surgery
7,000 due to medication errors in hospitals
20,000 due to other errors in hospitals
80,000 due to nosocomial infections in hospitals
106,000 due to non-error, negative effects of drugs
Based on these figures, iatrogenesis may cause as many as 225,000 deaths per year in the United States”
https://en.m.wikipedia.org/wiki/Iatrogenesis