Even if it would work out to distribute the pork across the continent, the fact is that all this splitting introduces logistical cost (shipping) as well as development costs (red tape needed to approve any change). SpaceX doesn't have any of that crap, and Tesla (with its famous ditching of the old school "auto makers and parts suppliers" ecosystem) either.
One of the stipulations for SpaceX to even have contracts was they had to support the space coast. They do. Launches from Kennedy are frequent and the drone platform the rockets land on are stationed there. SpaceX is the new NASA and like you said, they don’t have the red tape of having to justify parts manufacturing across the states.
The sad reality is in the US, too many towns were built around a very specific and niche business. Coal in the Appalachian mountains, NASA and the space coast, Pittsburgh Steel… it’s a community plan that failed and yet is still being used today. Woe to those that move/live there.