The problem isn't that a government funded research team is slower, it's that the private research team is in addition to the government research team. There are an uncountable number of illnesses and conditions that treatments could help with, but we have only so many resources to throw at these problems. Additional resources will allow us to find treatments for problems that we couldn't afford to research otherwise.

If the government invests $100 billion into medical research and private companies invest another $100 billion then we're probably getting more medical research done than if only the government invested $100 billion into medical research, and the private companies spent the $100 billion on making movies.