Earlier quoted context omitted.
Britain was only as eager to renounce slavery because they had no colonies that profited from it after American independence. Also, the rise of fascism in Europe was abated pretty effectively with an independent US anyway.
> "was abated pretty effectively" Ah yes, all of Europe occupied by fascists and a war with 60 million dead, nothing to worry about. Do you also consider the black plague "a minor public health issue, promptly addressed?"
First off, British America would have never had the same amount of territory that the US ultimately had; Napoleon would have never sold the Louisiana territory to Great Britain, the Southwest would still be part of Mexico, and at best the Pacific Northwest would have been part of Canada. British America would basically stop at the Appalachians, with Louisiana probably reverting back to the Spanish and becoming either part of a greater Mexico or existing as its own quasi-post-colonial dominion. So while America could be the breadbasket of the Allies in our timeline, that would have been impossible without American independence.
Secondly, Britain would have never allowed America to industrialize to the degree that we did, because they wouldn't want that kind of competition for their domestic industry. So not only are we no longer the breadbasket of democracy, but we're not even the arsenal of democracy anymore.
Thirdly, you're looking at a scenario where in the First World War, Americans would be drafted and shipped overseas to die pointlessly in the trenches or in failed offensives like Gallipoli. And you think this would make Americans more likely to accept future British demands to be drafted and sent overseas to die in another pointless European war? Since in this scenario British America never even reaches the West Coast, there's absolutely no chance of a Pearl Harbor, either, meaning Americans have absolutely no stake in the Second World War.
In other words, British America would be a much weaker country than the United States, with less land, fewer natural resources, less industrialization, less manpower, and much less will to fight. They would have been available two years earlier, but Britain and France just sort of sat around doing fuck-all between September 1939 and May 1940 anyway, and it's not clear that the addition of a small number of Americans to the BEF would have saved France. And it's even worse than that. Without the United States the Pacific theatre would collapse, with Japan likely holding uncontested access to the natural resources of the region and probably even capable of successfully invading Australia. In real life, Britain basically gave up on everything east of Burma. It was the United States who had the resources to engage the Japanese at Guadalcanal, effectively checking their advance and making their position in New Guinea untenable. In such a scenario, Japan would likely be able to more effectively project naval power into the Indian Ocean and concentrate their forces on the China-Burma-India theatre.
Finally, compared to the rise of communism in Europe, fascism was abated pretty decisively, with probably fewer overall deaths and in a much shorter period of time.