Offloading the risk on private players, reduces the amount of government investment required, and shields them from any criticism, should the project fail.
Also, if it is that strategically important, the government can just buy SpaceX.
They probably wouldn't have to buy them, if there's a war on they probably have enough legal tools to just require SpaceX to sell them whatever capabilities they have.
Also, if it is that strategically important, the government can just buy SpaceX.