The fact is, bringing a drug to market safely is a lot of work. All organizations respond to incentives, both corporations and governments. You can say it would be nice for the Government to do that work, but what is the incentive? In practice, most bureaucracies respond to incentives like individual actors minimizing their actual work and attempting to gain promotions. The practical incentives don't align very well with the work and risk associated with drug development. What bureaucrat wants to authorize the effort for a series of huge clinical trials for an experimental medication - they have a downside for failure, but not much upside for success.

This problem aligns far better with capitalism. Companies have incentive to do the work because they stand to make a windfall if they succeed. Governments don't.

I could be wrong of course. How would we test this? Well we have a pretty good free market for this right now - corporations are free to develop new drugs, and so are governments. Corporations develop lots and lots of new drugs at breakneck speeds. Governments by and large don't. Not that they never do, but it's a trickle, relatively speaking. If you want governments to develop more drugs, why not just do that now? Show us all how your solution can work.

The only way to do what you seem to want would be to actively prevent corporations from doing drug development work. So you would be actively preventing new drugs from being developed by organizations that are proven to be able to actually do it in favor of a setup that is demonstrated to work worse. In short, you would be actively making the world a worse place because you have some weird hangup about people making a profit off of something.