Lack of providers isn’t what’s driving up costs.
9% might also seem pretty big to me if it's out of all spending and doesn't include other provider compensation? What if overall healthcare costs went down, but physician compensation stayed the same? Would that then be a problem because it was an increased proportion of the total costs — fat left to be trimmed, so to speak?
There are many problems that don't have anything to do with providers per se, but I also don't think you can glean much by extrapolating to more of the same, especially compensation per se.
We don’t have to extrapolate from physician compensation though. We know that providers per capita have increased, but costs have continued to skyrocket. Therefore a lack of providers is not the immediate cause of the increase.
In addition to increasing the number of providers, the scope of practice for non-physician providers has almost universally increased.
All of this doesn’t prove that increasing the number of physicians wouldn’t lower costs some amount, but it does show that the increases over the last 20-30 years requires some other explanation.