Ah, you have to follow the money. Just nationalizing health care won't solve the problem, it will still be extremely expensive.
Insurance companies are not the leeches people think they are; they have a very narrow profit margin.
Most of the cost insurance companies charge is based on the cost of health care: doctors and hospitals.
There are some serious abuses occurring on the hospital level, like charging for things they didn't do, and overcharging for a box of tissues.. or, you know, charging you to let you hold your baby:
http://www.healthline.com/health-news/ridiculous-hospital-charges
There are a lot of articles on this if you look for them. It's not clear how common this nonsense is, but I've heard plenty of anecdotes and seen enough bills myself for ridiculous services.
Accountability and overcharging have to be reigned in somehow if spending is going to be reduced. Price transparency would help with that, and the only way we'll likely get it is government intervention.
But that's only part of the problem. There's a much bigger issue at hand.
There aren't enough doctors. Or nurses.
This causes two problems which influence spending:
1. Due to supply and demand, doctors are also paid MUCH too much (once they pay back their student loads, that is; a doctor fresh out of residency is not rich by any means due to crushing debt). You can hardly fault them for working for the highest bidder, particularly as med school costs kind of price set here.
2. Doctors are overworked, see too many patients, and don't get enough sleep.
The first influences your medical bill directly, and the second might kill you, and influences it indirectly. Being overworked is why so many people get hurt or killed in hospitals when doctors don't get sleep, and it's why (along with the U.S. litigious culture and a few blood sucking lawyers) liability insurance is so expensive.
When doctors and hospitals have to pay an arm and a leg for liability insurance, they pass that onto the consumer.
You have to pay more because a doctor screwed up because he or she was overworked and killed somebody and the family sued and the liability insurance company had to pay out millions of dollars which meant the hospital had to pay huge premiums which all had to be accounted for in the price of the service.
Yeah, lawyers are a big part of it. But it's not even all their fault. Doctors need to stop being overworked, but in order to do that we need more of them and finally I come to the last ingredient of high healthcare costs:
Inflated tuition prices (which I hinted at) for a medical degree (and the limited number of schools providing them).
Not only do student loans and just making back the investment mean doctors HAVE to charge more for their services right into the industry, but the barrier to entry (and limited spots) also reduces supply of doctors and nurses, meaning both that they CAN charge more, but also that they have to be overworked which meas they make more mistakes which means higher liability insurance forcing them to charge even more etc...
It pretty much all tracks back to education and the cultural failing to turn out more healthcare workers affordably so there's more competition and more people to do the work so they can see fewer patients and just do a better job all around.
You want to fix the healthcare issue?
Establish free government run medical schools, and maybe throw in a bit of tort reform while you're at it to cut down on frivolous lawsuits. Those are still a big issue. Something bad happens, and even if it
wasn't the doctor's fault families often look for somebody to blame (and sue). That has to be changed because the only ones getting rich off that practice are the lawyers (not that all lawyers are bad, but there are some leeches out there).
Nationalize or don't nationalize. Single payer would be more convenient in some ways (and I support a public option for that reason), but it won't solve the problem (it will be a modest improvement). We need to look to the root of the issue.