When a scarce resource is free in terms of dollars, other factors come into play that act as costs. Common methods are rationing, waiting times, social status, favors, donations, etc. Something has to happen to match up supply with demand.
People who can go to a doctor freely go sooner and don't (have to) wait until things get really bad - at which point treatment also gets far more complicated, lengthy and expensive, and that relationship is not linear. I don't need to wait until the tooth is truly rotten and now the jaw and bones holding it are impacted, because I have no incentive to delay and safe the expense, which is even worse for the many uninsured and under-insured.
I grew up in the GDR (East Germany) for the first 17 years of my life. While I turned out well, I had years and years of close contact with a large variety of doctors, for my eyes, sleep EEG, LOTS of small problems. I was a regular visitor of a pretty sizable variety of doctors in various places, not just the hometown.
The fears expressed hear from Americans about that kind of health care, to me, are simply ridiculous. The system worked darn well. I got soooo much, and I wasn't even all that sick, and that in a really poor country (compared to Wet Germany).
By the way, we did have a "top layer" of doctors (in East Germany) where you needed more (don't know if it was money or favors or if they selected you), who were far better than the normal ones. Still, nothing any more outrageous than now - the best are few, everywhere. Getting to them wasn't a matter of being rich though (I know because I got to see one or two of such top doctors).
Interestingly, a friend of mine found that getting the "top doctors" even now does not have to be a question of money. His wife got cancer and the standard treatment would have given her 6 months. He had money and brain, he checked the literature and did his research to find the best doctors relevant for his wife's case - and all it needed to get them to treat his wife was a few phone calls. Not a single additional Euro was spent, they didn't want any. They were cancer researchers at German university clinics, but he also checked with experts in the US. the experimental treatments she got and that gave her a few more years (instead of 6 months) were all paid for by the "Krankenkasse" (the common public insurance vs. private insurance, which exists too). They paid the huge sums without question but refused paying tiny amounts for small stuff...
For each medical condition, there exists a wide range of treatment options, all varying in efficacy, convenience, pain, risk, and cost. If cost were no consideration, why should anyone not get the most costly treatment available, even if it is only a minor improvement?
Most people don't behave that way. You seem to be assuming that people always want to squeeze everything they can out of a system but that's simply not the case in real life.
There are a lot of people who will only go when they need it, mostly men. For instance I have not been to a GP in probably 6 or 7 years. But I can see lots of people with chronic conditions (most of which could be prevented or reversed with lifestyle changes) going all the time. And it seems like the kind of thing where once you have a couple prescriptions, you're going in frequently to check in, and each time possibly adding new ones for different ailments you develop.
My Doctor-couple friends said it this way: There are three ranks of hospital: childrens' hospitals are the best. Next are womens' hospitals (maternity etc). Finally hospitals catering mostly to men are the worst, mostly because men are so indifferent to treatment.
