To establish whether the US insurance system as it exists contributes to the high cost of healthcare, you can simply look at any other country in the world.
Insulin costs around 100 times more in the US than anywhere else, for instance. This is not an accident, it is a product of the system, and how it works. And it works that way not just because of rapacious drugs companies, but because of the insurance companies that support it all.
The insurance industry is absolutely part of the reason that healthcare costs are so high, not the only one, but it is a system that relies on that insurance existing. Which is why the CEOs of those healthcare companies spend millions, and most of their time, ensuring that system continues.