The doctors who perform these tests are trained to understand this type of stuff. They're not just blindly accepting any single test result
They're "trained to understand this type of stuff" in the sense that it will get a mention in medical school. Overwhelmingly, they aren't "trained to understand this type of stuff" in the sense that if you pose them a simple problem of this type, they'll be able to calculate the answers.
> Next, suppose I told you that most doctors get the same wrong answer on this problem – usually, only around 15% of doctors get it right. (“Really? 15%? Is that a real number, or an urban legend based on an Internet poll?” It’s a real number. See Casscells, Schoenberger, and Grayboys 1978; Eddy 1982; Gigerenzer and Hoffrage 1995; and many other studies. It’s a surprising result which is easy to replicate, so it’s been extensively replicated.)
Edit: There is in fact another comment on this thread of someone doing exactly this: https://news.ycombinator.com/item?id=45652535
To answer your question directly I don't have strong feelings about it. I would prefer if they were freely accessible, other than maybe things like antibiotics that have clear externalities.
I'm okay with insurance companies saying they won't pay for them unless a doctor writes a script, but to gate keep relatively harmless drugs the way we do isn't my favorite policy. There are many times I would love to get a drug but don't want to talk to a doctor about it. This is one of the reasons companies like KHealth exist - they're just rent seeking on a silly system. You can get anything you want, you just have to jump through hoops, but all those hoops just make doctors richer and health care cost more.