I wouldn't go this far. Part of the current revolution in the private space industry is precisely allowing companies to own products that were partially funded by taxpayer dollars. As it encourages companies to fund their own money into it, rather than simply relying 100% on government funding.
Further if the government wants to encourage some industry, by using tax dollars to fund it they would instead destroy that industry. Many companies would end up simply refusing government grants because they know they could never profitably sell it if it would simply be copied. Or they would charge the government significantly more for the product.
Now yes, if the research is done at federal centers that simply exist for research rather than creating products, yes absolutely put it out for free immediately, so that it can get into products faster.