The US healthcare system is just fundamentally broken. Its not even about private or public. Even if they made it public, it would probably still be far and a away the most expensive system in the world.
People who believe that making it public will massively lower the cost because other socialized systems are cheaper are up for a rude awakening.
No matter in what direction the US system evolved those problems need some amount of addressing and those questions are more practically important then the question about public or not.