SpaceX's main innovation was that they decided to build a rocket that wasn't optimized for performance or reliability, but cost. They were willing to bear huge development risks to create a new price category and capture latent demand for cheaper launches.

I'd say what SpaceX optimises for most is iteration time. They have benefited hugely from an iterative development pattern contrasted to the waterfall pattern of NASA et al. Time is your biggest cost.

I'd say yes and no. You most definitely have a point here as I agree that their model, or view, is different than NASA. However, if NASA had not happened, would even conceiving of a different model or target had happened? Not to mention just initial research into rocketry. It maybe could have happened without NASA, but probably with a severely higher initial investment.

The soviets had a very strong space program and arguably their rocket designs have had a significant impact on spacex…

I should have included them also. It is very much a "standing on giants." As many scientists and engineers from different countries and nationalities have made major contributions. I believe it was an early soviet scientist in the 20s who came up with the formula for how much fuel needed to be loaded into a rocket.

Super Heavy does look a lot more like an N1 than a Saturn V, after all.