It should be at, or partnered with, higher learning institutions and since it's public funded all of the results should be free to use*. I'm willing to entertain the idea of: Free use for people and corporations within the country/countries that funded research, everyone else pays compulsory license fees.
https://ospo.gwu.edu/overview-us-policy-open-access-and-open...
https://www.nih.gov/about-nih/who-we-are/nih-director/statem...
https://www.coalition-s.org/plan_s_principles/
The intent of the Bayh-Dole Act was to deal with a perceived problem of government-owned patents being investor-unfriendly. At the time the government would only grant non-exclusive licenses, and investors generally want exclusivity. That may have been the actual problem, moreso than who owned the patent. On the other hand, giving the actual inventors an incentive to commercialize their work should increase their productivity and the chance that the inventions actually get used.