You are kidding me... right? EVERY government plan, regardless of where it is, rations care.
So you think the government will deny coverage? That is not my experience with Australian health care.
What is a fact is private health insurance companies can and do deny valid claims. They can and do set a lifetime limit on coverage. When something major happens, people often are forced into bankruptcy. IMO this kind of crap is unacceptable.
In general I am for free markets, but when it comes to the health insurance industry, they have shown themselves to be a detriment to society.