@meiosis let’s define what is meant by “government involvement”, shall we? In many countries in the world I can walk into a pharmacy / druggist / chemist and buy drugs that I can only acquire in the US with a doctor’s prescription in hand.
In many of those countries, and others, I can also freely pick my “healer of choice” without regard for whether or not the person is an actual licensed M.D. or not. I’m sure that I could also hire a well-qualified nurse overseas to do things that only MDs are legally allowed to do in the US.
Many newly developed drugs are available overseas long before they’re approved for use in the United States. (I’m well aware of at least one time – from the 1960s, I believe – that the FDA still trots out to justify the incredibly long and convoluted trials that are required to be passed in the US before a new drug can be introduced to market. Thalidomide was a one-off.) No one can effectively count the number of people who have died while waiting for a drug that might have saved their lives, but still had years to go in testing before they could even consider taking the chance with what was left of their lives.
“Government involvement” means a lot more than “who is paying”.
We also need to define “better outcomes” (and find a control group to represent the various populations we’re checking, one against the other), but let’s start with the first definition first.