Or he will have to change his rates, or not retain patients with chronic conditions (For this to work, the doc has to have the option of not renewing a patient who has a chronic condition at the end of the year).
For other patients, it is reasonable to assume that illnesses and accidents will be fairly evenly distributed over the year, and that this month's payments can be used to cover this month's expenses.
You have described an actuarial (insurance math) solution. I think NY State is being foolish. But it is an insurance-type product.