As far as I know, a big flaw with your system is that the care that you receive is frequently decided by the insurance company rather than a medical professional.
That is largely the case here, at least in some aspects.
At my job (and I assume generally in my field), we get all happy when we find out that the people who will be reading our requests for authorizations for more visits have clinical experience (and will therefore understand why we're saying yes, yes this person does need more than 12 visits with me per year). This actually come up at team meetings "Well, the people reading your requests have clinical experience." "Yay!!!"
Which is to say, we generally don't assume insurance coverage is determined by experts rather than bureaucrats unless we're explicitly told otherwise.
Though come to think of it idiot bureaucrats determining policies on things they know nothing about is what's wrong with a lot more than just healthcare in the US.