As far as I know the uninsured do not pay higher prices, they pay at best on a cash only basis which is lower, or they pay nothing at all. The insured are picking up the difference.
I don’t go to the doctor often, so maybe that’s different, but when I lost my dental insurance, the price that was charged went up about 80%. So basically a “free” checkup that the insurance paid X for, cost me almost 2X when I lost my insurance and had to pay out of pocket.