Starship isn't largely a government project. It was planned a decade before the government was ever involved, they came along later and said "Hey, this even more incredible launch platform you're building? Maybe we can hire SpaceX to launch some things with it?"
Realistically, SpaceX launches far more payload than any government.
Source: I am out of LEDs and LASERs and now handle aerospace solar for a private company. Guess who almost everyone in the private sector flies on?