You really can't imagine that decoupling the profit motive from drug research is possible?
Research funding is allocated mostly by the academic community itself, via panels consisting of academics. This does have problems of its own, but they have little to do with politics as in elected politicians. Policians can have some influence on general directions, but it's quite limited.
What you say sounds very much based on the general anti-government and anti-democratic ideology rather than evaluation of history.
The large increase in non-traditional funding orgs for biomedical research over the last several decades has been driven by a widespread perception that the traditional government funding has been increasingly captured by a academic cliques with low ROI priorities.
I've worked in government science orgs, the capture of funding control by ideological academic cliques is very common. It has unfortunately infested the biomedical research funding, which reduces realized ROI from the money allocated to those orgs. In the US government, some of the best medical R&D ROI dollar-for-dollar right now is found in the military, but that really shouldn't be their job outside of traditional areas like trauma medicine.
Not if it goes through the traditional grant process. I've fundamentally soured on that.
Maybe an open bounty system? First one to develop an effective drug for X gets their costs paid for + 1 billion or something (number pulled straight out of my ass, feel free to adjust)
But even that would be better than the current system where people that have nothing to do with the research get obscene amounts of money solely on the merit of having obscene amounts of money.