You are correct SAN has the separate line and let me assure you as a 1K I want it and use it!
I rarely need the check-in counters at LAX but when I do the lines are a complete mess and the Premier lines take longer then the general lines. I use LAX as a connection point with United but avoid having to connect through LAX for international flights returning to the USA. I do fly using LAX for OALs I just do not understand why LAX is such a mess landside for United.