There is only one detail I cannot understand. Why competition doesn't work? Why some new investors (who are not invested in drugs yet) do not invest in the research of new drug that heals all the diseases, to sell this drug for $1 -- they would destroy existing system, but they would get all the market at once. (Or in a smaller scale they might make a drug that treats some disease once and for all, and shrink not the pie overall, but some part of it).
You might even argue that the money saved by not having a patent could be used to save even more lives.
4. Nobody makes any attempt to create a treatment, but after only six months a miracle occurs. Nobody dies and everybody is cured for no reason.
Not saying that there isn't any, but where is the evidence that a government funded research team would be slower than the privately funded one?
If the government invests $100 billion into medical research and private companies invest another $100 billion then we're probably getting more medical research done than if only the government invested $100 billion into medical research, and the private companies spent the $100 billion on making movies.
Let's say we have a disease that kills 1000 people per year. Let's look at a 40 year period.
1. No cure is researched or found in 40 years. Total death count: 40,000.
2. For the first 10 years no cure is found. After 10 years a company comes along and creates a lifesaving cure, however it's expensive - only 500 people per year can afford it. The patent on it lasts 20 years. After 20 years another company creates a generic version of it that 990 people can afford. In the first 10 years 10,000 people die, in the following 20 years another 10,000 people die, in the last 10 years 100 people die. Total death count: 20,100.
3. No cure is found in the first 20 years, then a government funded research team finds a cure. A company picks it up and creates a generic, where 99% people can afford it. In the first 20 years 20,000 people die. In the latter 20 years 200 people die. Total death count: 20,200.
Being early matters in medicine. It's always easy to look at an expensive treatment and say that this should be much cheaper, but we usually don't consider that forcing investors out of healthcare means that less research will be done. This means fewer treatments and a longer time before a treatment is found.