Senator Elizabeth Warren says yes, because patent protection gives drug companies monopoly power that they exploit. Her suggestion raises several issues.

First, Warren is right that while patents might incentivize innovation, they also keep prices elevated while new drugs are under patent, thereby reducing utilization. Patent policy should seek to balance these two effects, and current policy might not be the right balance.

Second, Warren’s suggested policy - more government, rather than reduction or elimination of existing patent protection - fits the standard progressive approach: assume the fix to imperfect government is more government, rather than less. 

Third, libertarians are divided over government patent protection. On the one hand, libertarians endorse a government role in defining and enforcing property rights generally, so why should intellectual property be any different? (And as a bonus, intellectual property protection is an enumerated power). Further, standard economics suggests that private investment in new ideas might be insufficient without patents.

On the other hand, the current patent system generates a non-trivial frictions: patent trolls try to “hold up” firms that might use patents for new products. This causes no ineffiiciency if Coasian bargaining costs are zero, but that seems unlikely. 

Existing research, moreover, provides little evidence that patent protection spurs innovation (although pharma may be an exception).

So, Warren raises a valid concern over patents. But rather than having government manufacture generic drugs (what could possibly go wrong?), why not just scale back existing patent protections?