There is no guarantee that a health system that requires individuals to pay for their treatment leads to better and more efficient services.
Healthcare companies are not required to reinvest their profits in their product. They can, and do, funnel that money to owners and shareholders without using it to improve their product.
In a private system, there are also still barriers to the best treatment options. The only difference is these barriers are financial. Under both systems, a poor person without insurance cannot access the best treatment options available.
Having more care doesn't mean better care. Private companies have an incentive to have more patients and charge to dispense more drugs, more surgeries, more expensive tests. But doesn't mean the system has better outcomes for it; it simply makes more money for hospitals, surgeons and caretakers.