Why wouldn't SpaceX turn into the funding and political football that NASA is, if it were nationalized?
Like, this isn't a hypothetical. SpaceX only has a market because of the incompetence of the "public option."
That's quite inaccurate. NASA doesn't do much themselves, they hire external contractors but keep significant control over them. SpaceX got more funding and less control and they didn't start from scratch, NASA gave them all of their technical documentation, now-how and working prototypes.
NASA could have done everything SpaceX does if they were given the same conditions and funding, however, they've never had funding for blowing up five spaceships in row, they were held to much stricter standards.
The entire story looks like a blatant attempt to take control of space operations away from NASA and thus from the government.
This may have been hypothetically possible, as are many things that never came to be, but it is impossible to know whether this really would have happened.