I've been on all 3 sides of this debate. As a consumer, an insurance agent, and now as a healthcare provider. If you seriously think that there is just one solution that benefits everybody then you aren't seeing the big picture. You have to balance the idea of maintaining an advanced research and development of medical equipment, techniques, etc... The best way for that to happen is a profit based model. That creates revenue for those things. You have to keep the consumers healthy to start with, that is a role I would like to see the government expand a bit. Preventative treatments/screenings/education. You have a moral obligation to your seniors who carried the nation, again a government/societal role, and you have to make sure that providers are able to afford to have careers to efficiently deliver healthcare, which both private and government models can provide through profit based models for increasing pay, and licensure/verification by the government to make sure that the healthcare pool does not become oversaturated with incompetent providers.
There is no reason to eschew on for the other. Both models should be used for what they can provide to the entire healthcare model. There is more at stake than just tax payer dollars, or insurance premiums. There are industries, jobs, and careers on the line as well.