There is actually a long history of doing exactly this. In short, the government (correctly) believes that it is not very good with creating business, and it is better left in the hands of the private sector.
In terms of the ownership of the intellectual property, the extent to which these NIH/NSF Grants reach ends with the discovery of the knowledge. These Grants are not considered benefits or entitlements, but awards to support specific public purposes. It is a form of transfer payment from the government. You can consider it a lever for the government to support selected fields of research, but no more than that. These Grants are designed specifically to not entitle the funding agency ownership of the discovery.
The government is determined to help the scientists and the institutions to turn the discoveries into businesses, because only through business can these insights gained from research benefit consumers. There are specific grants for this purposes and they have in the past been successful at helping brining discoveries to market, creating viable small businesses. The idea is that the ownership of the intellectual property is best bestowed upon those who were involved in the original discovery. And it is best to leave the creation of businesses to the private sector, because the government is not very good with creating businesses directly. If you are looking for an examples of government being inefficient at running business, you can look at the nuclear power industry. It is completely government owned because of the obvious homeland security implications. Yet it continuously operates at a loss.
As a side-note, to address your comment on "universities train these specialists":
these specialists are not trained by the Universities. These specialists are the universities sans the administrators, There won't be Harvard without these PI's. Also, knowledge is useless on paper. It is these specialists who knows how to use these knowledge who are valuable. Just to give a sense of how rare(and valuable) these specialists are, in physics and biology (where I have worked), I noticed that in most of the fields there are usually less than five lab and their corresponding PI's who are contributing 95% of the most cutting edge work.
Marie-Anne Paulze Lavoisier, his wife remarried to a rich publisher after Lavoisier's death, who supported her to publish a lot of the work. (both awesome people)
David, the guy who painted this portrait was the person who signed Lavoisier's guillotine papers. The story goes David was an amateur scientist, had some presentations, and was humiliated when Lavoisier make it clear that it was pseudo science. David wanted to be elected to the royal society but because of this never got to. He was a friend but thus became the enemy.
He also painted the painting "death of Marat". He himself was executed a year later.