Mathematicians,physicists also do a lot of research and they do not ask you to pay them to use their findings.
Say you find a cure for X, how will you price it as a company? You put some variables into an equation and attempt to get the maximum profit not the maximum health for the society. This could mean letting poor people to die or suffer without a cure.
Yea, this sounds like an awesome idea. Let's do it.
What? of course they do. The moment a physical reaction or process is applied to industry, you can bet someone will file a patent.
At engineering school, it is common for professors, students, etc, to patent technology they invent. Colleges have entire departments.
What I am thinking is this, the smart people that want to become scientists do not do it to make money for some company, they do it for passion and help people in the case of people that learned to become doctors and research medical treatments. You need a system that finds this smart people when they graduate and place them in research institution paid by the public. You can have private companies research other stuff but don't put all the core research into private companies that are motivated of making profit. You have for example the military founded by tons of money that some of them go into research, my suggestion is have health research similarly prioritized as the military. You could even pay private research institution but when you pay for research all the results get put in the public domain.