The problem for some of us in the USA is that we have seen government health care run the USA way. I lived under IHS (Indian Health Service) for a big chunk of my life. They came about 6 hours from killing my Dad and my brothers records "disappeared" and he has a mis-diagnosed back. Google "don't get sick after june" for the typical problems. I myself had a botched root canal (3 surgeries afterwords) and lesser back problems.
Given this, I don't see how they can be more competent with more people under the system. If you cannot get it right for 1.2% of the population, you are not going to get it right for the rest.
That said, there are some things government could do that would help everyone. A "cataclysmic" insurance modeled on flood insurance to take care of costs over a certain dollar figure payed out of the taxes we already pay. Cut the cost of drug approval and work out longer term cheaper payments beyond the patent life. Tort reform for drug approved for the FDA. Scholarships for every nurse and doctor keeping a decent average. Reduce the cost of filling out government paperwork. Loans to needy individuals to pay their healthcare bill, payed back to the IRS.
I'm not very optimistic because I haven't heard any politician looking at what the actual input costs are for health care and trying to reduce those. They seem to accept health care costs will stay high.