To walk away from an alliance would have made Japan a threat.I see your point. But after the defeat of Russia by the Japanese in 1904-05, the Russians were not a threat to anyone really in the Pacific. The Germans however did have a presence in the Pacific that I would assume the continuation of the Anglo-Jaoanese Treaty would have been a benefit or otherwise why continue? Unless Britain considered the US a threat?
It's would have been considered a major insult to Japan to walk out from the alliance.
Also during the alliance Japan became a major trading partners for military technology. Between 1/3 and 95% of the components of every IJN vessel was purchased (or licensed) from the UK. That had a massive economic effect.
As to British forces in the western hemisphere, well quiet simply those were in decline since the end of Napoleon. The Jamacia station was merged into the North American and West Indies station (Bermuda and Halifax) in 1830. In the latter part of the 19th century it wound down.