At least in the US, government policy has meant that getting a drug to market is an extremely high bar. This means that funding the wrong drug can waste a billion dollars or more of time, material, trained researchers and lab space, etc.
Funding drugs by popular attention, private donation, kickstarter, or anything like that is likely to produce a bunch of scams and even more waste.
Funding drugs by having the government select which ones to study is likely to produce several gigantic financial boondoggles that are dragged on because some Senator wants the jobs wasting the money creates to remain in his state, or something.
If we want more drugs to come out, the best thing to do would be to reduce the cost of making a drug legal to sell, like by lowering the proof required for efficacy, or by alleviating the doctor shortage by permanently increasing the number of medicare funded residency slots.