Pharmacist and 4th year medical student here. Medical tests are ordered based upon their statistical ability to alter your likelihood of a diagnosis. No test is perfect in either direction (negative result meaning you don't have disease or positive result indicating you have disease). Tests cost money, take resources of the healthcare system, and have the potential to be wrong. When a test is wrong, it can result in financial, emotional, and physical harm to an individual.

Example: you're an otherwise healthy 34 year old and you feel a little under the weather and are coughing. It's only been going on a few days, mild fever, but you're worried and you go to the doctor. Your doctor thinks this is most likely a viral infection, recommends Tylenol and ibuprofen and sends you home. You imply to the doctor you'll sue if you don't get antibiotics and a chest x-ray just to be safe. The doctor, rather than argue with you when they have a dozen other patients to see, just orders the stuff and moves on. The chest X ray doesn't explain your cough, but there's a small lesion of undetermined significance on the X-ray. Now you need a CT. The CT says "probably a self-limited granuloma from a fungal infection, can't rule out cancer, correlate with biopsy". Then you have to go get sedated, put a camera down your throat, and have a pulmonologist take a sample of your lung to see if you have cancer. Maybe you end up with a complication from the sedation or a pneumothorax. Meanwhile the antibiotics you took didn't really improve your cough but now you have this uncomfortable itchy rash. Are you allergic to the amoxicillin? Or did you just develop the typical rash seen in people who have mononucleosis that also take amoxicillin? Will you get allergy testing for the amoxicillin? Just avoid amoxicillin, an awesome antibiotic, for the rest of your life?

We are restrictive in our prescribing of medications and tests not because we don't care about you, not because we want to save the hospital or the insurance company money (in fact the hospital prefers we order more things because they make money on testing). We are restrictive because we want to maximize benefit while minimizing risk, and everything we do has risks and benefits.

Because tests have harm. The average persone doesn't understand what the sensitivity and specificity of a test means.

Yeah, great question, I don't understand it either, but marginalized groups like women or people of color can have a hell of a time getting medical professionals to take their concerns seriously. Maybe it's just a hubris thing. "How dare this person question my judgment when I'm the doctor?"

Well I'm guessing that the healthcare will pay it. And at least in Switzerland, the healthcare can announce official that they won't pay anymore for anything that one doctor decides/order. So if the doctor orders to many thing, that the healthcare has to cover, then he soonly will lose his job. So in this way the doctor will only order stuff that are really needed and maybe won't make a test against cancer (but this happens not really often)

Else if the customer has to pay, then yes it would be stupid to not let the customer do the test.

Possibly Kaiser, or similar, where they're the ones paying themselves which is somehow legal?

There are some tests that can do harm to patients. In this case obviously a CT scan should have been ordered immediately, but not every pt with a cough needs a fat dose of radiation.