Because trade secrets are virtually impossible in non-biologic drugs, the entire funding ecosystem around pharmaceuticals is driven by patents.

5 minutes of googling suggests that Penicillin was not patented and the mass production was later patented by the USDA (not some private pharma company). The entire modern funding ecosystem being patent based just means it's the most profitable business model, not that it's the only way to produce pharmaceuticals.

https://en.wikipedia.org/wiki/Penicillin#Mass_production

https://patents.google.com/patent/US2442141

Some drugs likely would be discovered through non profit efforts. But it seems reasonable to believe that we would be quite a bit farther behind overall without the profit motive.

Of course it’s not the only way to produce pharmaceuticals, as pharmaceuticals are thousands of years old. But without patents the number of new drugs pharmaceuticals over the last 50 years would be probably 1-5% of it actually was.

Maybe we would have less but better pharmaceuticals, because it would be easier to improve the existing ones.

The way the system is set up now, there would be little incentive to make pharmaceuticals without patents. The R&D cost is insane, so to be profitable, pharmaceutical companies need exclusive rights to their drugs.

Bearing that in mind, I have no reason to believe a fully state-funded pharmaceutical system would be impossible, tied into healthcare. However, to make people complacent with that, it would have to be unbelievably transparent. Many people fear the idea of the state designing and providing them with drugs.