If doctors are not a major part of the cost, then saying "hospitals and doctors are a major part of the problem", while technically true, is disingenuous. It's like saying "Stalin and and his cat killed more than twenty million people" - technically true, but it assigns the cat an unwarranted part in this problem.

Two separate points were made. The first is that the numbers of doctors is limited in order to keep salaries. Which is true. The second is that hospitals and physician/clinical services were the majority of health care costs in the US. Which is also true. See link.

All the rest of the logic you supplied yourself.

Since you seem intent on sticking words in my mouth, I don’t think doctor are necessarily paid too much, and don’t think limiting their salaries will substantially affect health care costs. I do think doctor salaries probably will go down if their ranks weren’t artificially limited, but society would benefit, and doctors might too with a reduced workload. In fact, the overall proportion of medical costs given to physician salaries will likely go up if their ranks weren’t limited, albeit with each individual doctor making less.