I have catastrophic insurance to cover unexpected circumstances and enough money in an account to handle normal, day-to-day healthcare. In setting up my finances in this way, I am able to cover myself and not have to fork over a premium every month. This has saved me thousands of dollars over the years, if I compare the current premium I am obligated to pay with my previous strategy of putting money into an account.
True insurance is a hedge against risk, I looked at my risks and made the rational decision that covering myself was the better decision.
Its not for everyone and so I don't want to generalize. I just offer it as anecdotal evidence that while increasing the percentage of the population that is insured, may be a nice easy metric to measure and affect, it is not necessarily an indication of improving situations for all Americans.