I wonder if a system like that could work.

SpaceX and numerous other companies were able to draw in billions of dollars of funding for R&D to chase after US Government contracts that could only be won by proving massive technological feats (reusable rockets, etc).

Hypothetically, it seems we could do something similar for drugs. Instead of "If you make a medicine that works, you get a monopoly to sell it for X years" it could just be "If you make a medicine that works, you get a check for $X, and then the drug is immediately generic".