Outright war is unlikely
But a better US opinion is probably worth more to Britain in most circumstances than the AJA
Say Italy acts up, which is the most probable strategic threat one can see in 1920, or Germany does. Britain can deal with those easily enough on their own, and neither would result in the activation of the AJA. So in effect no benefit to having it. Whereas it existing may push the US in that situation from Friendly neutral, to true neutral or even to unfriendly neutral and make Britain's life somewhat more difficult
The AJA can only be activated if Britain ends up at war with two or more Great Powers, which is unlikely given the relations as they are in 1920, the USSR is a pariah, as is Germany, France and Italy dislike each other. And even if they get involved, well how valuable is it really? In WWI Japan took what territories they wanted, then sent a token force to the Med. No Japanese Divisions served on the Western Front, or at Salonika, or in the Middle East, or in Italy, no capital ships served with the Grand Fleet or escorts in the North Atlantic. Arguably not a very valuable Alliance, and arguably less contribution than a friendly neutral US made prior to 1917
And then of course there is the what if no war situation? At which point having a better inclined US is worth something economically, while the treaty is worth nothing
Well the argument is that better to have Japan onsides than not. But what does Japan get out of it? They can pretty easily beat any two powers at sea that don't include the UK herself, or the USA, Russia might be a problem on land, but the USSR has no allies thus the AJA would not apply to a conflict with them. So the only use to Japan is in a conflict with the USA, to prevent someone else from taking advantage but Britain said the AJA does not apply to that in 1911. So Japan is functionally getting nothing out of the deal. Therefore if they are inclined to be belligerent to Britain and her Empire, why should they keep the Treaty? And if Japan decides not to renew the Treaty asa prelude to aggressive actions, well all Britain has done is made the US less happy with her for no gain