From an economic standpoint, universal health care coverage makes the most sense. Canada spends less than 75% per capita on health care than the US. The reason is the insurance pool is much larger, diversifying away more risk. Also, needless procedures are reduced, as people can't "self-treat" using their private coverage. Doctors are in charge of prescribing services, so there are no HMO accountants denying someone coverage.
From a human standpoint, allowing all members of your society access to high quality health care shows that you have progressed past the point where every aspect of life is "survival of the economic fittest." We never have families bankrupted by enormous medical bills.
The Canadian model has private suppliers belonging to the public program. This way we don't have the imposed caps on salaries that providers in other nations have. We still do lose some medical staff to the US, but that is an overblown problem. Many doctors have found their income in the US not much higher when the cost of operating their infrastructure was factored in. The reason we lose nurses has nothing to do with the health care system, but a gov't attitude that nurses were expendable, and they left in anger.
No system is perfect, and it's possible to find flaws with all of them. However, we've had a system that has worked pretty effectively for decades and most folks in Canada are more than pleased with the system. Want to rile up a Canadian? Suggest US style HMO-based health care.
Now, before you yanks throw out the old "rich people deserve better care because they're rich" statement, realize that not every nation or culture believes that.
1998 C230 "Black Betty"