The real problem is that health insurance is overly expensive - mainly thanks to the relationship between gov / insurance. You should fix that; thinking that nationalising health care will fix the problem is just some politician's dream. The extra money needed for nationalised health care will have to come from somewhere - and because poor people don't have money and rich people are too good at eluding their tax obligations, the usual middle class will pay for it.

I'd rather have a fully private market without national entities messing with the prices and charities for those who can't afford it.

Of course, no politician will ever champion such a system, because it removes the gov from the equation, making them less powerful and needed by the masses that keep paying taxes.