The first function (i.e. insurance in the classic sense, similar to car or home insurance) can be accomplished beautifully by the private sector as long as government stays out of the way. If there were no mandates requiring health plans to cover certain things, then premiums for a basic, catastrophic insurance plan would almost certainly be affordable to most healthy individuals. They could thus purchase a basic insurance plan and keep it for decades, not having to depend on their employers for health insurance, and not finding themselves suddenly uninsured if they lose or quit their job. Whatever happens, I think we will need to move away from employer-provided health care, simply because global competition will make it unaffordable for most companies.
One problem with this, of course, is that people with chronic conditions or past medical problems get screwed. Those who require regular medications for chronic conditions (e.g. Type 1 diabetes, bipolar, etc) would have enormous out-of-pocket costs. People who have had problems in the past (i.e. cancer, genetic heart problems) might have their premiums go up so high that they couldn't afford it. Another problem is that it gives somewhat of a financial incentive for people to wait until they get really sick rather than seek preventative care. One obvious example is maternity: if lower-income women have to pay out-of-pocket for all maternity/prenatal care (or switch to a more expensive health plan that covers maternity), a lot of them will probably decide to skip it. That of course could have really bad consequences for the babies. One could make the argument--and many on the left have--that subsidizing preventative care results in huge medical savings for society as a whole. That's probably the reason behind a lot of the mandates on coverage for maternity, routine checkups, etc.
The second function (making regular medical expenses more affordable) IMO cannot be accomplished by for-profit companies. It simply makes no sense: what service could they provide that would have any value toward accomplishing that goal? Right now, most people's health care is subsidized--but by their employers, not by government. Since it is subsidized for virtually everyone who has it, people naturally demand more of it--even more than they need--and health care costs go way up. Arthur Laffer calls this concept the health care wedge, and blames it for most of the runaway increase in health care costs (http://online.wsj.com/
article/ SB1000142405297020461900457432 4361508092006.html). And there is still the problem of people with pre-existing conditions being unable to get coverage. The only way to fix that, of course, is the way Europe does it: with an individual mandate, which is almost certainly unconstitutional. IMO, ObamaCare is even worse than a public option like in Massachusetts, and may be even worse than a single-payer system. Not only does it have the individual mandate, but it also puts a huge burden on small business which suffocates job creation.
One way to make health care work might be to separate it into two pieces: catastrophic insurance (which would be private) and subsidized care for the poor or those with health problems (which could be subsidized by nonprofits, large corporations, or government). That way far fewer people would have subsidized health care and costs would not go up as much. Of course, tort reform and eliminating state barriers would also help keep costs down.