American did have some 747's since 1970, they were among the first customers to get it, belieive it or not. In the 1970's, American had 16 747-100's which were flown on high-density domestic routes (JFK-LAX for example) but they had a terrible experience with them. Let me explanin this: American always had a strong domestic network which at that time consisted of 707's, 727's and DC-10's. But because of the oil crisis in 1973, the 747 was not efficient anymore to operate on domestic routes. The 747-100 was very fuel thirsty and the jet fuel price was increasing dramatically. So it was obvoious that the DC-10, which AA launced and got in 1971, would fit better in the domestic network than the 747 would. In 1984, the last 747-100 was phased out. Two years later, American acquired 2 B747-SP31's from TWA. Those 2 747's were put on the daily DFW-NRT flight until 1991 when the first MD-11 came. The 2 747's were then put on transatlantic flights out of JFK for one year, they were phased out in the mddle of 1992. Since then, American has had no more 747's of any variant. They have never had any 400's.
They have chosen the 777 over the 747-400 because they know that the 777 will be more efficent for them to operate (fuel efficiency, load factor, ...) . So why doesn't American have any 747's? The answer is there is no need for them to operate such a high capacity aircraft on the network that they have. The 767 and 777 fit much better.