Based on the info in the r/spacex thread where all of this was first posted, it seems like this facility is mostly for developing the prototypes of the BFR/BFS before the vehicle goes into full production.

My guess is that your second thought about their rocket building expertise being in LA caused them to choose LA for the prototyping and that a BFR/BFS factory at Boca Chica or Cape Canaveral is still a distinct possibility.