You can't lower costs by making something free. Come on.
But, the problem with healthcare is basically three things. It's an aging population, monopolies and the over-use of medicine as opposed to healthcare.
You can't really do anything about an aging population. Except there are things on the margin like so-called death panels, aka conferences with your doctor when you're about to die. People need to be better informed about end of life care and whether it's worth it to spend $400k to live an extra 2 weeks in extreme pain.
We have a system where doctors and health providers get paid when they provide medicine, procedures, surgeries, devices, etc. So, we over-incentivize medicine, procedures, surgeries, etc. For that reason, we give people tons of unnecessary healthcare for no good reason. On top of this, normal economic competition doesn't happen because people lack information and the ability to choose. Here's a great article that explains this point:
http://www.newyorker.com/magazine/2009/06/01/the-cost-conundrumThe final thing is the big monopoly problem. The medical profession is a monopoly that prevents new medical schools from opening to protect doctor salaries and keep them artificially high. Big Pharma is a big oligopoly. And, within each area of the county, a few big providers/health systems and insurance companies are usually monopolistic. You have to get control of those monopolies and professional cartels with better regulation.
Basically, we need a basic health insurance that provides access to very cost-conscious care provided more by nurses and lower-credentialed health professionals as a basic line of defense. That ought to be free to everyone, no exceptions. Then, you have Obamacare type exchanges for supplemental insurance that provides more care. This ought to provide tons of information about providers, cost, patient reviews and outcomes. Finally, you find a way to deal with the monopolies, either by breaking them apart or some other sensible regulation.