That's the system we had in the 1970s (government owned the patent to government-funded research). And what happened is that the government didn't know what to do with the patents, and the inventors, who were best positioned to commercialize their invention, could not justify spending time and money to commercialize something that they didn't own. So the Bayh Dole act of 1980 allowed universities to commercialize their federally funded inventions. The result was an explosion of startups, especially in the biotech industry.

Example: John Adler received some government funding to develop Cyberknife (image-guided radiation therapy). But he couldn't get follow up funding to commercialize this revolutionary new technology. So he took out a second mortgage on his house to commercialize the invention. And now image-guided radiation therapy is a standard treatment for many types of cancer. There's no way he would have taken out that large personal loan, if he didn't own the intellectual property.

There's a large gap between a patent, and a commercially viable product. And if you showed the patent to "experts" in the field, they would likely tell you that it's worthless. Great ideas are only obvious in retrospect. The inventor has the vision, motivation, and knowledge to make their invention a reality, but they can't quit their job and get external funding, if they can't own their invention.

The research results should not be patentable. If someone wants to then productize the research, they can patent any methods they can independently come up with, as long as they didn't use public money for that as well.

That is plenty of latitude for seeding start-ups and commercializing technology. There is no need to lock up the actual research so that only the researcher and their university can commercialize it, protected from competition. It does a disservice to the people who's money paid for the research behind it.