You sure? I don't have my guidebooks any more, but I dind't think 1580 was a high-power allocation channel.
Bear in mind that almost all the LA AM stations are using directional transmitting arrays (antennas). The directional arrays are there to protect other stations on the same or adjacent frequencies in other locales. A lot of the 50,000 watts radiated by KFI, for example, goes out over the Pacific, to protect other stations to the east on the same frequency. If KBLA WAS 50KW, it would probably have some other direction pattern that could keep it from making it to San Diego - if there were stations in SD or northern Mejico on the same or adjacent frequencies.
AM stations, BTW, achieve their directional patterns by means of multi-tower tuned arrays - and the engineering required to achieve a perfectly-tuned pattern is so arcane that there is an entire cottage industry in DC of engineering consultants whose job it is to come up with the precise gear needed to achieve a particular directional patter - and thus get the FCC's license approval. They don't just do this for US broadcasters, of course - that would be too limiting. They also design arrays for shortwave int'l broadcasters around the world. And that's ALL they do. Very arcane little industry.
Michael