> If you're rich, you have concierge medicine, and you'll see a great specialist whenever you want.
You don't need to be that rich to go see a doctor privately in eg the UK. And, yes, they have crazy queues for the NHS, while the same doctor can be had for a bit of money quickly when seen privately.
In that case, the price restriction comes from what the NHS is willing to pay. And because patient don't directly pay for the NHS, at least not proportional to the usage, instead of rationing via price the system rations via wait times.
> [...] the amount of medical care that would be medically useful for the population.
I'm not sure there's such a thing. There's no clearly defined amount that is 'medically useful'. There are just gradually diminishing returns to more medicine (in a statistical sense).