This isn't connected to insurance at all.
This actually prevents doctors who are specialists from seeing cases that could be handled at a lower level for much less money and many less tests. I see this as a way to REDUCE the costs of health care.
Now - I also believe in a capitalistic free society I get to see whomever I want whenever I want for whatever I want. And probably you CAN find that kind of specialist who is willing to take your money, when you could be seen by a General Practitioner or Internist much more cheaply to determine if it's something they can solve.
For example *most* Reproductive Endocrinologists won't see a woman who is TTC until they have been TTC for a year, are high risk or are over 40 (at which point it's after 6 months). This is because MOST of the time you want but don't *need* the bazillion dollars worth of tests that will determine there is nothing wrong with you, you are just impatient. Or that will tell you there is no reason for your 2 miscarriages... because there is no medical reason for your 2 miscarriages.
If the office has a policy get a referral from your regular doctor. If you don't have a regular doctor then you may need to look for a specialist in whatever specialty doesn't require one.... or establish a relationship with a General Practitioner within that system.