In terms of why the public funds research, your statement might be true, but isn’t addressing the concern that many in the public have raised before: the results of the research should be public, given that the research was publicly funded. We have laws about open access to government functions, so why is research different?
Yes this is what I meant. We fund research because we think pure research is valuable. It needs to be done without requiring a financial return. Products sometimes come out of it and that's also a public benefit, but direct results of the research are not a "product" they are the starting point to a possible product. There is still a lot of development that has to occur to get to the product stage.
Also you could argue that patents are open access. The whole point of a patent is you give a complete summary of what the invention is and how to replicate it (with a level of detail that would allow someone knowledgeable in the field to recreate it) in exchange for a time limited legal moat.