Does the Mexican government get its own say in what carrier gets the route?
Of course, though I have a feeling they usually just go with what the DOT agrees with.
where all can you connect to on AA from LAX?
Auckland, Boise, Brisbane, Denver, Dublin, Eagle County/Vail (Colo.), Fresno, Hong Kong, Honolulu, Kona, Las Vegas, London, Lihue, Maui, Medford (Ore.), Melbourne, Monterrey (Calif.), Nadi (Fiji), Osaka, Palm Springs, Portland, Reno, San Diego, San Francisco, San Jose (Calif.), San Luis Obispo, Santa Barbara, Seattle, Sun Valley, Sydney, Taipei, Tokyo, Vancouver, and Zurich.
Those don't include the "back tracking" connections, like Fort Lauderdale, Miami, New York City, etc., but those could be made too.
Continental, including codeshares, offers logical connections only to Gunninson (Colo.), Honolulu, and Tokyo.