Again, the end result is a decrease in the number of drug therapies available to doctors. Instead of multiple options, where one can be selected that best fits an individual patient, you'd have one. If that therapy works for the patient, fine. If it doesn't, if that patient fits outside the bell curve or stops responding to it (as is very, very common across a wide number of therapies), then that patient is screwed. And often, dead.
Just look at antidepressants, where doctors have to slog through a huge number of different options (not just different classes, like SSRIs or SNRIs, but often radically different drugs within those classes) to find the right drug therapy that works for each individual patient. Choosing the right medication, and the right dose (which can have a huge effect on how the drug functions) can mean the difference between someone living a healthy, productive life and suicide.
Drug R&D is an entirely different ballgame than basic science. And there's already countless examples of how basic science funding, from appropriations to attempts by politicians to interfere with the grants process, can be screwed up. Hell, just the amount of funding necessary to replace private drug R&D would be a significant political expenditure. And here's a fun consequence: how long will it be until some arrogant politician comes along and complains about how drugs developed with American taxpayer dollars are being provided to foreign countries? I can see it now, and it's terrifying: some bullshit slogan like "American drugs for Americans" should terrify you, too.
Even under the best case scenario, public funding would mean tradeoffs: research option A or option B, but not both if there's any overlap. And that's before politicians start playing games and before budget cuts start impacting research. Maybe the solution is to have manufacturer bids be sufficient to cover those R&D costs? Congratulations, you're right back where you started, with drug costs either the same or negligibly less. And where does the money go? If it goes into the state's general funds, politicians will use that money for their own special interests and pet projects. If it goes into an earmarked fund, politicians will cut back taxpayer funding by an equal or greater amount. You can see textbook examples of each with federal infrastructure funds and education funding in states that host lotteries "for the children."
Simple idea in theory, horrible in practice. Unintended consequences are still consequences.
As for antibiotics, that's a bit of a different case. There are a lot more arguments for public funding in these sorts of circumstances, where pharmaceutical companies can't research and bring a drug to specific, niche markets. Antibiotics are a classic example, especially when you consider the broader public health risks associated with the rise in antibiotic-resistant strains.