Well, yes and no.
Keep in mind that the reason Southwest is so big at LAX is because they filled the void that PSA and AirCal left. The succeeding airlines (PSA and American) did not sustain the level of operations that OC and PS had. Back then, WN was little more than a "new start" with only a fraction of the flights they have now.
At that time, PSA ruled the Intra-California market. Back in the 80's, PSA MD-80's and BAe 146's were as common at Terminal 1 as the Southwest planes are now.
Plus, being located so close to runway 24, they have easy access to fast departures.
As for whether or not any other airport could sustain some of all of that traffic, IMO the only one that MIGHT would be Ontario.