I think it would make more sense to simply have a government owned corporation who's sole purpose is to produce generic drugs on which the patent has expired.
Some drugs, like the cure for Hepatitis C, need to be available more widely before the patent runs out. It's a cure and only people that can come up with $84,000 dollars.
(The dustup over Martin Shkreli raising the price of Daraprim only happened because there were very few users of the drug)