Just as a heads up it's not really necessary to say things like "don't answer this with pure speculation" on this sub. You should check out the subs rules and look at some other posts. Speculative answers are removed.

But to answer your basic question "What was the purpose of the Balfour Declaration" I think you need to re-examine your assumption that Britain had "imperialistic designs on the entire region." That sort of depends on what you mean by "imperialistic designs." British leaders knew, from a very early point in the war, that if they defeated the Ottomans that they would be in an almost historically unique position, presenting both an opportunity and a challenge, to wipe the slate clean in the vast Arab territories of the Ottoman Empire. So in that sense, sure, they were designing. And I think you could argue that that mindset is "imperialist." But, by no means did the British imagine that the entirety of this territory would be integrated directly into the empire as some kind of Arab India, which is what your question seems to suggest.

The fact is that this British "re-designing" of the region was quite a drawn out process which lasted, in strict border-drawing terms, from the DeBunsen commission on British war aims in 1915 to when the last of the borders were concluded in the Treaty of Lausanne 1924. Between those dates you had a whole string of promises and treaties, the most famous of which is probably Sykes-Picot (which is often mistakenly used as a short-hand for this whole process) but that also includes the Hussein-McMahon Correspondences and the Balfour Declaration.

I think one way to look at this incredibly long process of treaties and conferences is: "whose aims were being accommodated and/or what promises were being promised to whom in each treaty?" In that view the DeBunsen commission described Britain's own, ideal war aims. Sykes-Picot was a set of negotiated promises to the French and was in tandem with a parellel set of negotiations with the Russians. Sevres carved up Anatolia for a whole host other smaller war partners. The King-Crane commission was to appease the Americans. San Remo was to appease the Hashemites. Lausanne set up final lines with the newly founded Republic of Turkey, France, Britain.

From that perspective I very much understand your confusion over Balfour because "the Jewish people" weren't a major imperial partner like the French, or a belligerent like Turkey, or even a non-state actor like the Arabs involved in the Hashemite-led Arab revolt.

Unfortunately given the premise of your question and what you seem to think would be credible the best explanations and the only ones that I've come across that make sense are the non-strategic ones. There were prominent Zionists with strong connections in the British government like Chaim Weizmann (who had discovered a chemical process key to British munitions production and was therefore critical to the British war-effort) who advocated strongly for a Jewish homeland in Palestine. There British gentile romantics or practicing Christians who in large part by virtue of a biblical education and culture simply thought that the Jews must have a home in Palestine. One of the more interesting groups were something like Zionist anti-Semites. This group believed that basically Jews either controlled the world, or at least the United States, and that proposing the creation of a Jewish homeland in Palestine might get international Jewry on side. Many of the British Zionists played this up. Herbert Samuel, the British post-master general and a Jewish Zionist wrote in a cabinet memorandum that the goodwill of "a whole race may not be without its value." Weizman would write trans-atlantic cables to US Supreme Court Justice Louis Brandeis playing up the idea that Jewish influence could turn whole fronts in the war seemingly for the sole purpose that British censors or intelligence would get hold of the cables and buy into the idea.

The irony in this of course is that many, perhaps even most of Britain and America's Jews at this time were actually anti-Zionist or at least non-Zionist. "America is our Zion" and lines to that effect was a common refrain of many American Jews.

It's also worth stopping and considering what the Balfour Declaration actually says and how it was viewed. I've mentioned above that I would make the argument that the British did not have absolutist imperial designs on the entire region, but even if you want to argue that they did the Balfour Declaration does not actually contradict that, at least as it seems to have been understood at the time.

The actual text of the Balfour Declaration reads:

His Majesty's government view with favour the establishment in Palestine of a national home for the Jewish people...

A national home in Palestine was emphatically not understood by the British government to mean that Palestine would become majority Jewish, or that there would be a Jewish state, let alone an independent Jewish state. With hindsight a pro-Zionist British policy that doesn't involve the creation of an independent Jewish state seems almost naively self-contradictory, but then so does the very next line of the declaration which reads "that nothing shall be done which may prejudice the civil and religious rights of existing non-Jewish communities in Palestine". It simply was not understood by British policymakers to be a problematic issue at the time. It was a freebie promise that would have no consequences.

The same was true of the United States which voted affirm the Balfour Declaration. In the congressional testimony of American Zionists who advocated that the US support the declaration it was argued that Palestine was basically empty desert and the Jewish emigration to the Palestine would benefit not only the land and its current Arab occupants by virtue of Jewish industriousness but also relieve the United States of having to take on more European immigrants (or at least Jewish European immigrants) because they could go to Palestine instead. These advocates made it very explicit that US support for the declaration would not entail the guarantee of a new independent Jewish state in Palestine.

So I think the TL;DR answer is that, from our perspective, there don't appear to many very good realpolitik strategy reasons for the Balfour Declaration. It was a partially romantic partially anti-semitic notion about gaining Jewish support or restoring Jews to their ancestral homeland. It was also believed that, like many of Britain's other war time promises that it would have no real consequences or commit Britain to any actual policy or otherwise limit British aims in the region.

Source wise:

Tom Segev's One Palestine, Complete goes through many of the machinations of British Zionists like Weizman to gain support for a Jewish national home in Palestine.

The congressional debate on supporting the Balfour Declartion was held in the Foreign Affairs Committee from April 18-21, 1922 and can be found in that respective volume of the record of the House Foreign Affairs Commitee.

On American Jewish support for Zionism in the 1910s-20s see Howard Sachar's "A History of Jews in America."

On the long series of British imperial negotiations in the Middle East see D.K. Fieldhouse "Western Imperialism in the Middle East".