They invented this using money provided by the taxpayers so it belongs to the taxpayers, i.e., the people. How could they possibly get a patent? I could only see it as a step to get an international patent to prevent other countries from utilizing this without payment. But any company in the US should be able to make it without royalties.
You are sadly uninformed about patents and use thereof.
First, the inventor(s) get credit for the invention.
Second, the patent is “owned” by the individual or organization employing the individual(s).
How the patent is exploited may well benefit your taxpayers but we are not socialist and society does not have any rights to this intellectual property.