True, but I think there's also the propaganda victory of having a Jewish force take Berlin.
Now you could have the British raise the Jewish Brigade a lot earlier, or even have Ze'ev Jabotinsky not die (the below paragraph is from an old post of mine referenced
here). A Jewish army is raised in 1941-42. After all, Jabotinsky was the force behind the Jewish Legion in World War I, along with Joseph Trumpeldor. The biggest issue is that the British would be reluctant to raise a Jewish army, the Americans are isolationist, and Weizmann & Ben-Gurion would be cautious of the Revisionist movement. But if they come to an agreement with Jabotinsky, Ben-Gurion, and Weizmann to have it like the Jewish Legion in the First World War, it might be acceptable.
But let's say a Jewish army is created in 1941-42. Jews would be fighting in a Jewish army, under a Jewish flag (which the British wouldn't like, as they rejected Weizmann's offer). In his June 19
speech in Manhattan, Jabotinsky said, "There is stuff for well over 100,000 Jewish soldiers even without counting American Jews...that source alone would have yielded three to four divisions." We're talking about thousands of trained Jewish soldiers and officers, possible involvement of former members of the Jewish Legion, and the Revisionist movement most likely would even put forth a platform for rescuing European Jews from the Nazis and funnel them to Mandate Palestine.
I could see two main ways this Jewish army could be involved in fighting the Nazis and have a shot at taking Berlin. The first is being attached to the British in North Africa, and then getting diverted through Italy northwards. The second is being attached with the British when they land at Juno and Sword Beach and move through Nazi-occupied Europe. Maybe a race to reach Berlin first?