It might depend on your definition of "best." World Health Organization ranks France #1 and Italy #2. US has a solid #37 rank. Healthy life expectancy, US ranks #24, health system performance #72 and preventable deaths #14. The fact is having insurance is no guarantee that you will receive the services you need.
I don't think giving everyone access to some sort of health insurance means more people will go to the doctor. People already abuse the system as is and it ends up costing us more. If you do not have access to a doctor, due to lack of insurance where do you go? To the ER, via ambulance based on my experience. So rather than going to your doctor for care, you incur an ambulance bill and ER bill. That cost ends up getting passed on to the taxpayers. The drug seekers will do anything to get their medicines. Healthcare needs to shift to a "preventative" mentality and give people affordable access to treat medical conditions early before they get out of control and end up costing more to reverse or treat. Diabetes and high blood pressure are the best examples. Both can lead to cardiac conditions, stroke and renal disease and both can easily be controlled (diet, exercise and medication) when identified and treated early on.
I personally would like to see health insurance overhauled to include covering pre-existing conditions and not denying claims to save money. It should also be made cheaper. How, in a recession, are insurance companies making billions of dollars in profits? If you pay someone money for insurance, they shouldn't have an option to deny your claim (unless its fradulent). A public insurance shouldn't be available to everyone. It should be available only to those that don't have another insurance. Here's an example, someone that is a reservist in the military is not eligible for the Reserve Tricare if you are a federal employee and receive insurance through your work. Makes sense, if you already have insurance why do you need a cheaper government version? Reserve Tricare is administered by Humana South (private company).
Again, the problem isn't giving the uninsured access to affordable or free healthcare, its how the program is run. I am all for public health insurance, but it has to be run effectively and efficiently even if that means involving private companies.
Do you think issuing every US citizen and legal resident a medical ID number, separate from their social would be a good idea? And anytime someone that comes in to the ER and doesn't have a medical ID number should then be deported for being here illegally?