Funny you bring that up, because 27% of all US Government systems run Linux. The problem is that the government doesn't give back any money, or contribute much code to the FOSS projects that they rely on. If they gave back proportionally like Linux Foundation Platinum sponsors do, they would get a return on their investment just in that they run enough Linux to benefit from contributing.

China has given money to FOSS projects far more than the US does, and there is an official Chinese Linux distro available to Chinese users. Nobody is forced to use it, outside of Chinese government employees on their work machines, but like a library, it is something of value that the state can provide to those who might need it.