The government does frequently fund the discovery of new drugs. The problem is that the return on that investment is usually abysmal and the taxpayer ends up not only paying to fund the drug’s discovery, but also paying absurdly high prices to buy it from pharmaceutical companies who passed some or all of their risk onto taxpayers.
Of course. Most of basic science in the US is government funded. I'm wondering what the OP thinks about removing the barrier that they identified (private corps paying for the trial vs gov paying for the trial) and how that would affect their thinking.
The government is the whole reason the clinical trials are required before patients can be treated with a working drug. They are the cause of the problem, not the solution.
One example: https://abcnews.go.com/WNT/YourMoney/story?id=129651