I'm not arguing the medical system isn't flawed, but you can't oversimplify it by saying "Corporations are evil, so let's have the government do the work." Nothing in life is simple, and nothing in life is fair.
Joe, I got no idea how old are you but from my perspective I can say - yes, we should oversimplify flawed things, especially when it concerns common good and gov.
Let's make a simple, hypothetical calculation with a looong, boring introduction.
Doctors and nurses here earn as much as a car mechanic, though their job is much much harder, and they cannot live with what they earn if they work in a public health-care places. They decided to go on strike and there are massive quits, also nurses are occupying lawn in front of prime minister hq for prolly a month now. They want to earn around $1500 / €750 a month, now they get like half of this sum. Doctors are earning a bit more, but not much more.
To make a full picture, you get a free health-care when you are full-time employee with contract for an indefinite period of time, otherwise you must make an agreement with your employer that he will pay your social contributions, and that simply does not happen, because no-one wants to spend more money than it is needed. You also get access to medical services when you are under 18, over 18 but studying on a state university and also when you are a pensioner or simply old aged and retired. All in all, health-care services are public and easily accessible, at least in theory.
To add some real-life touch-ups - 5 years ago I broke both side-ligaments, attaching my knee to a muscle. My knee was 4 times as big as usual, I couldn't bend my leg and all that nice stuff. Of course, being a wild hardcore warrior I decided it's perfectly ok to wait 3 or 4 days, and the knee surely gets back to a normal shape, which of course wasn't true. When I couldn't stand the pain and a knee wouldn't want to cooperate at all I went to an emergency, got the knee punctured, they took loads of liquid out of it (like massive 15 ml or something, 1 and a half of big syringe, so whoa - and a nice miss told me to visit orthopedist immediately. It was june. The earliest date was like in the end of september. What did I do? Of course went to a private doctor, paid something like $30 / €15, he touched my leg in two places, looked at the rtg photo, told me to come some other day to plaster the leg, and that it is better to visit him while he has a service at a public hospital. I went there and guess what - I could get whole leg plastered the oldschool way, with gypsum, for free or pay another $150 / €75 to get nice, light-weight 3M plaster that you can bath with and it will eventually dry. I paid, of course. So the whole cost was $180 / €90.
What is funny, at that time I had a full time contract and I payed around $2000 / €1000 a year to have an access to a public health-care services (not even mentioning other taxes, they took like 40% of my monthly wage, bastards). What is wrong then, if I pay, you pay and he pays too, where is that money? Why the docs and nurses don't want to work? Why you hear that there is no date for 3 months, though you can go to a public hospital to have a private visit, and during whole time this orthopedist was "on duty" nothing happened, no-one came?
Now for the calculation. Polish parliament got 466 members, all of them got mobile phones, I'm betting any money for these are not payed by themselves but from our taxes. Let's say they pay $150 / €75 a month which is not much concerning how expensive mobile services are here. Now let's think - hey, what would happen, if they could pay like half for themselves? 466*(150/2)=466*75=$34950 a month.
They are here for 4 years, that is 4*12, 48 months*34950=$1677600. w00t. Divide by 1500. It is 1118 moths of new, "high" nurse wages. No more questions.
So I say, these gov folks are simply wasting our money here and there (this quick mobile example was the first thing that came into my head, but I bet they are making much larger sums of money disappear in more idiotic ways) and there is no reason we would not get a free, easily accessible and high-level health-care, because there is money for it. As Foo nicely pointed out, it is about a "proper" insurance system, where folks pay the money, but they got something in exchange, and the ones that cannot pay can also get help when in need.
One can visit the hospital once in his or her lifetime, right after the car crash that could happen to anyone and it is goddamn duty of government to save lives of their citizens. It's not about ethics, it's about social order. With whole respect to you Crowjane, I say this one is not connected to any background.