Obamacare did do some good things that needed to be done, but essentially, everything about it was a bandaid intended to kick this shitty system down the road to the next person who had to deal with it. But hey, at least health care companies can't just turn you down because you have Diabetes or are too fat anymore.
http://www.vox.com/2016/1/17/10784528/bernie-sanders-single-...
The difference is that with most socialised systems there are two system in parallel:
A public system whose priorities set based on measured impact, rather than by . E.g. in the UK, a separate agency develops guidance independently that measures how treatments affect "quality adjusted life years".
And a private system, whose priorities are, like in the US, based on how deep your pockets are.
For the vast majority the public system is the only one they use, but about 10% pay for private insurance. In practice this acts like a good indicator:
If takeup goes up it means more patients believe NHS care is slipping and makes them feel they need to "top it up".
If prices goes up (private insurance here is exceedingly cheap, since most providers are based on you going to the NHS first and then referring you privately if you e.g. don't get to see a specialist within X days) it's an indicator the providers see NHS as deteriorating (causing more claims from their customers).
The US could do the same - continue to allow private healthcare, but cover a certain level of treatment via a public system.
Edit: Let me also add this; when you sign up for health insurance you're entering into a contract with the insurer. They have to be up front about what they're providing and it's your obligation to understand what you're buying. With the government you don't get that. You get whatever the vanilla flavour of healthcare coverage is today. There's no contractual obligation, only whatever the government says is right today. You don't get a guarantee. Because there's no contract you can point to, even if you're legally allowed to sue (and I don't think you are.) you won't have a case to stand on.
There's an enormous information and power imbalance in the health insurance contractual relationship. The large number of medical bankruptcies by people that had health insurance is surely a testament to this fact.