As PJ O'Rourke once said, "If you think healthcare is expensive now, wait till it's free!"
I agree that part of the problem with healthcare costs is that no one want to pay for anything. We are no longer using health insurance to insure against unforeseeable, catastrophic events, but rather want it used for anything healthcare related. It's like getting car insurance and then expecting that your gas, oil changes, wiper blade replacements, tire replacements, etc. are also all covered. If that were the case, everyone's auto insurance premiums would have to go up, perhaps to the point that people would rather go without insurance -- even for the unforeseen accident down the road. And when you start having people leave the insurance pool, the average cost for the rest in the insurance plan will also go up.
I understand the idea behind a government-run healthcare system... To ensure that the cost-per-user is at its lowest, you want the largest insurance pool. For example, if you had 1000 people in your insurance pool and 1 person had to go to the ER for a $1000 procedure, each person in that pool would have to pay $1 to cover that event, whereas if the pool only had 10 people in it and that same person went in for the $1000 procedure, now everyone would have to pay $100 instead of $1 to cover it.
The problem however is that with health insurance set up to cover everything, many people are paying for things that they don't need, and people are also more apt to use the services even if they don't really need it. If auto insurance were set up the same way, you'd have some people that drove electric cars paying more to cover everyone else's gas consumption. And because no one has to pay for gas out of pocket, they're also more apt to go through it much quicker, driving their Hummers and SUVs just to go to work in their office. This also exposes another issue with having insure cover everything; people don't see the expense so they don't care, even if the cost-avoidance would create other benefits besides the financial aspect. If people didn't pay for gas out-of-pocket, they'd be more apt to consume it the same or more, whereas when people do pay for their own gas, they become more conscientious of gas prices and so may try to carpool more, use public transportation more, or even ride a bike or walk. And by using these other forms of transportation, they additionally are reducing their pollution footprint and are not reducing the supply of gas as much. Similarly, if people had to pay more for out-of-pocket healthcare costs, like having to pay for annual visits, medication, etc. they may actually try harder to exercise more or eat healthier to reduce their out-of-pocket costs for more check-ups and tests for their diabetes and / or heart disease, and in addition they are living a healthier lifestyle so will have a lower risk of some more serious ailment down the road.