One issue is however that the actual costs are not so much in early R&D (what the publicly funded universities and hospitals are doing), but in the later stage (clinical trials) which needs deep pockets and appetite for risk, which only big pharma has, because they see a potential big payout.
Let's just cut out the middle man.
It is so bad that for a lot of treatments, getting them to people costs upwards of hundreds of millions of dollars. And almost all of these efforts fail.
This would mean the government would need to breed (and pay for) lab animals, small and large (from mice to primates). Would need to pay more for medical care, would need to collect (and pay) people to try out experimental drugs and treatments on. If these treatments or drugs have adverse effects, the government would need to shoulder sometimes lifelong payments and care to these people. It would need to cover all this knowing that in 90% or so of cases the whole effort was for nothing.
This is, to put it mildly, not happening.
Taxpayer money has paid for a substantial percentage of research around the world, and it doesn't seem necessary that we rely on profit-driven private companies for the actual therapies when they could be done at publicly funded hospitals too.