Limiting doctor availability is an effective way to limit total cost because most expensive health care goods and services require a doctor to order or prescribe the good or service. I.e, until the patient gets enough time with a doctor for the doctor to realize that the good or service is necessary (then prescribe or order it) the insurer does not need to pay for the good or service.
Limiting the supply of doctors will increase costs in the long run because it reduces access to preventive care. Residency caps disproportionately impact PCPs.
It might reduce the costs they pay for preventive care or non-urgent care, but serious issues will progress.
You might not have to pay for metformin to treat diabetes, but you’ll eventually end up paying for a hospital stay and amputation.
Your proposed incentive for insurance companies to want to restrict the supply of doctors (prior to the ACA) doesn’t make sense, and that’s what I’m trying to convince you of.