Also, some places where funding matches are used to bring stuff to fruition would lose significant funding from both sides: private would not in many cases invest where the results would be given away for free, and govt could not invest or match to help bring things to market.
For example the SBIR program would face significant problems, and it's responsible for a lot of good research and products. DARPA stuff would face the same issues.
Or, to keep such stuff not public, groups that currently publish would simply not publish in order to get funding to continue working. Then the public again loses access to knowledge.
Also, there is no such thing as zero cost - someone is going to have to pay to make such materials available - and that cost (even though small) will likely be borne by the taxpayers. For example, arxiv costs a few million a year to run.
Such solutions are unlikely to yield the results you want.