Patents weren't the issue. As I recall, Shkreli's company had the exclusive right to market the drug in the US, regardless of patent protection. For example, the FDA provides regulatory exclusivity that prevents generics from entering the market even after the patent expires. [1]

Patents were a collateral issue. On that collateral issue, one of the issues with patents is that drug companies have a tendency to stop producing drugs towards the end of life of a patent to force patients onto a newly patented drug. This practice could be stopped by allowing generics to produce, market, and sell when the patent holder will not.

[1] https://www.commonwealthfund.org/publications/journal-articl...