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?
Optimization is literally how contractors working for the government got rich. Every hour they spent on research was directly billed to the government. Weight reduction being one of the most important and consistent points of research.
Heck, R&D is how some of the biggest government contractors make all their dough.
SpaceX is built on the billions in research NASA has invested over the decades. It looks like it's more innovative simply because the USG decided to nearly completely defund public spending in favor of spending money on private contractors like SpaceX. That's been happening since the 90s.