Delta not only faces a competitive disadvantage without a hub on the Tokyo end out of Haneda, but also offers limited connections beyond LAX as the return segment arrives into LAX in the evening. Nevertheless, by virtue of being located on the West Coast, as well as catering to a large amount of Origin and Destination traffic between the US and Japan, Delta is more likely to stay committed in fighting it out for LAX-HND. The slot times, while not ideal, are also not as terrible as they were for Detroit on Delta or New York JFK for American.
Morever, Delta CEO Richard Anderson has been bullish about not only securing improved hours, but also shifting Delta's Intra-Asia hub, inherited from Northwest, from Narita to Haneda. Some are skeptical about whether he has been pragmatic in approaching Japanese authorities with the appropriate tone required for his actions to become effective, but he doesn't show any signs of backing down. He certainly got his way with allowing the US DOT to grant him a second chance with Haneda from Seattle, so never say never.
Second, while OneWorld considers LAX a cornerstone "hub," in reality, the alliance holds a mere 22% marketshare, outpaced by Star at 28.3%, and followed closely by SkyTeam at 18.5%, according to CAPA. Conversely, at SFO, by an large considered Star Alliance' premier West Coast hub, Star maintains a 55.2% marketshare, followed by SkyTeam next at 10.3% and OneWorld at 8.9%.