No government funding of American healthcare is nearly 67%.

"Tax-funded expenditures accounted for 64.3 percent of U.S. health spending – about $1.9 trillion – in 2013...  The Affordable Care Act will push that figure even higher by 2024, when government’s share of U.S. health spending is expected to rise to 67.3 percent."

"At $5,960 per capita, government spending on health care costs in the U.S. was the highest of any nation in 2013..." http://www.pnhp.org/news/2016/january

And per capita the government funding of healthcare in the US is the highest of any nation.

So answer the question. Why is it reasonable to assume that "more government involvement" will result in "good or better health outcomes than we do for less money"? 

Answer honestly and specifically address the question. Because someone else can do it is not a reasonable assumption. Nor is removing insurance company profit as the federal government already controls a large percent of American healthcare.