The American health insurance industry is completely fucked if you think it has anything to do with providing healthcare and isn't entirely about maximizing profits for the inner circle. People are literally dying because we have the least efficient health insurance system in the world. And it's designed that way because some people are getting ridiculously wealthy from other people's pain and suffering.
Then check with your state's attorney general. In many states, insurance companies are required to provide it at no cost. Certainly in the last three states in which I've lived.
If it's not required in your state, then contact your legislators and try to get a law passed.
For example, the first back injection was denied the first time one the basis that "it was not inhibiting her daily function". The notes from the doctor submitted to insurance specifically said "the pain in her back is inhibiting normal daily function." They reject it just to see who will fight back. Furthermore, insurance is only required to look at notes from appointments and will ignore comments from doctors if they aren't tied to anything. So in order to fight an insurance claim requires another appointment with the doctor which costs more money just to get the insurance company to look at the claim again and get it approved.
It's a terrible game.
These tend to make financial sense for insurers - flu shots are cheap and a lot cheaper than hospitalizations, same thing for avoiding pregnancy... and even then, both were explicitly made free via the ACA, not the kindness of health insurers.
These aren't the sorts of claims insurers kick up a fuss over.
Worthless political echo chamber hyperbole and demonstrably false.
Just off the top of my head: Virtually every American with health insurance can get flu shots for free, paid for by their insurance carrier. Ditto for women who want birth control pills (though that is usually a legislative mandate).
A friend works for a small insurance company, and she says it paid over a billion dollars in claims last year for fewer than 50k members.