I'm not convinced that the govt bureaucrats would do a worse job than drug co bureaucrats. Current studies are poorly designed, implemented incorrectly, results are cherry-picked and gamed, p-hacking lives, ... This is an industry that can't even seem to accept pre-registration.
Also, as you say, most of these molecules come from publicly funded research. Why would the group funding the first set of research (and producing more molecules than industry) automatically be bad at the second?
In all, I'm not convinced that "Drug discovery is the easy part." If it was so easy, then why don't drug co's do it, and save the licensing fees?
Because licensing costs less and is risk-reduced?
People have different motivations and talents. Woz is a great computer engineer and Jobs was a great salesman. One without the other wouldn't have given us ubiquitous personal computers.
Same thing applies to organizations.
In theory the government could nationalize the entire pharmaceutical industry but there is no evidence that bureaucrats are capable of reliably picking the right candidate drugs. Countries with weak IP protections do relatively little new drug development.