UA have a few flights, my understanding is that AA have rights but don't exercise them, continental used to have flights as did alaska iirc. Problem is that the real money on that route is in business travel and the american airlines can't compete in terms of product, the biggest competition qantas has is air nz. To be honest to _really_ get some competition there would need not only a decent airline such as singapore flying transpac but there also would really need to be a *A airline flying domestically in aus.