I’m not sure the race between government entities and the private sector always favors the former, even when it comes to R&D. A prime (no pun intended) example of that is the race to sequence the human genome.
I don’t think that’s the example you think it is - HGP was a US government project. Private companies went on to commercialize gene sequencing, but the R&D was started by the public sector.
To be fair that's lots more money involved and needed in nuclear research. Of course that the private sector can also get hold of that amount of money but because of the way greater sums involved it needs to "show results" sooner rather than later.
Those using government funds can label it as "military research" or something similar and then they're looking at a least a few decades of no-one asking them where the money went and why.