Public money pays for the roads. After the road is built, the road belongs to the public. Public money pays for the research. After the research finishes, the results should belong to the public, the same way as the road does.
(i) e.g. privatization of telephone networks
(ii) e.g. toll roads and bridges
The 'public' wanted that by voting in the lawmakers making that possible.
That's how democracy works.
Also we're not talking about physical things, but something 'intellectual' like software, so the comparison is inaccurate.
More accurate would be IT research done in a publicly funded university.
Depending on where you live, you could very well be under the impression that the roads belong to delivery companies, taxis, etc. (private companies that make money off them) as they are effectively useless to everyone else (= the public) while they are constantly blocking them.