The problem with the private sector is that there are legal methods of increasing profits and successfully competing other than innovating and providing the best service/product.

It's much easier to capture a regulatory agency, or find a way to breach contracts under the pretense of fraud, or benefit from perpetual antitrust exemption that allows you to price gauge your customers.

If all of those things were illegal and the laws enforced, corporations would have no choice but to compete on the value of their product/service.

If this were so, it might be a good thing to keep the health sector private, competing and innovating better and more cost effective methods.

In advocating for public health care, you presume that the cabinet members appointed to administer the program will be motivated to continue to improve upon the status quo.  Perhaps they would.  

But it's also likely that, as with other publicly administered programs like schools, there won't be enough will to improve on a system that "works" well enough already.

As for financing, I'm all for public financing of health care.  But when it comes to the administration, I'm not sure what I think.  Either way I have to rely on the government, either to regulate the private sector or run the program themselves.  If this were a country of well educated, sensible people who elected thoughtful, hardworking, honest representatives, I'd be 100% for public administration.  But as it is now, I think it might be nice to keep politics away from health care.

No, it is not. We award a monopoly to a single heavily regulated water company because it would be prohibitively expensive and mighty inconvenient to have the streets dug up and pipes buried three or four times so we could have competition between water companies. Hospitals and insurance companies don't dig up the street to pipe health care to my house.