Let's say that the US does not get bitten by the Empire bug in the late 19th century remains isolated from alliances and interested on in enforcement of the Monroe Doctrine and trade only.
Might we see a world of three competing alliances instead of two - an Anglo-Japanese alliance with Japan having a free hand in the Philippines and North China/Manchuria, with mutual support elsewhere in China. Britain is navally dominant in the West and Japan in the East with neither vulnerable to invasion. The British cannot look to a more preferable friendship with the US.
We still have the Triple Alliance of Austria, Germany and Italy and the Dual Alliance between France and Russia.
France and Russia are the Anglo-Japanese competitors (in Africa, the Near East, the Middle East, the India frontier and in China). If Britain had a solid alliance with Japan which included an intervention in the Russo-Japanese war for example, ending hope of a rapproachment with Russia or France, how might Britain maintain a balance on the continent without it?