I thought the Anglo-Japanese alliance was primarily a Asia Region specific alliance. Not so much against the US as in curbing the ambitions of Imp. Russia vs their possessions in Asia. In this case Imp. Russia would not exist and a new focus for the alliance would be needed. Aiming it a curbing US expansionism in the Pacific is blatantly stupid given that they are all allies from the previous war. However, I see no reason a purely regional defensive security arrangement could not have been done. Such a move would at least on paper have given NZ and Australia some security against any aggressive moves against Br. Imp possessions.
Such an agreement could give Britain and the dominions some "small " influence over the foreign policy of Japan through the late '20's early '30's moderating to some degree such that WWII in the Pacific does not even occur as we know it. A defensive agreement that was followed up by some kind of Economic co-operation agreement would have alleviated to some degree Japan's need to expand to gain its southern resources directly.
AuroraBorealis
That is totally accurate. Only the more extreme American navalists, desperate for a reason for their naval expansion plans that pretended the alliance was directed against the US. [Along with anyone ignorant enough to have believed their propaganda of course

]. It was initially directed solely against imperial Russia which was a threat to both powers. In the 2nd renewal in 1911-12 Britain even went as far as giving the US a way to attack Japan without invoking the alliance but the US Congress dropped the ball! By the tail end of WWI Imperial Russia was no more but there was growing concern about the Soviets and also a defensive alliance is always useful so it was short-sighted of Britain to have agreed to cancel it.
The alliance did give Britain and the dominions influence over Japanese policy, as well as establishing good relations between the navies especially of the two nations. That was one reason why the Australasian dominions were generally in favour of continuing it. While it was in place they were safe and secure and Britain didn't need to fear about their interests in the Far East and Pacific.
If Britain had stood up to the US over the alliance and preferably also a more responsible Naval Treaty, some in the US would have been unhappy but the more responsible would have got over it pretty quickly. There might have been some sabre rattling by the hot-heads but they would have got stepped on pretty quickly. Anglo-American relations would have then been placed on a healthier and more stable footing than the US assumption that Britain will always make sacrifices to meet US whims. It may also very likely have avoided the bloodshed that occurred in the Far East in the 30's and 40's. If say the depression had still drive the Japanese into militaristic expansionism then the alliance would have been terminated then and Britain would have been in a better position.
Steve