Hi Raul,

TL;DR, there wasn't any political will to.

Longer answer, I think there's reticence for a couple of reasons.

First, I think it's important to remember that the western allies had just fought through the bloodiest war in human history together, with the Soviets shouldering a lions share of that burden. Suddenly turning upon the ally you've built up as a savior of Europe would be difficult enough, let alone one you've also hyped up as being an unstoppable steamroller of an armed forces.

Second, people are just absolutely sick of war by 1945. This has been a titanic life-or-death struggle that has pushed the populations of many of the allies, particularly those in Europe, to their absolute limits. The countries are in ruins, the population is exhausted, and they've all been working towards this great final goal of 'defeating Nazi Germany'. Once that mountain has been scaled, they aren't expected, or willing, to climb another one. You can sort of see this is Labour's victory in the 1945 elections, where they'd focused on an idea of 'now win the peace', and defeated a Conservative campaign that leaned much more heavily on its wartime record.

Those two factors make it much more difficult to rouse people to supporting further war, but what makes it almost impossible is the lack of an immediate, clear, and present danger to the western allies from the USSR. While we nowadays have an image of their regime as murderous and perpetually poised to sweep across Europe in a wave of tanks and Grads, the horrors of the soviet regime, and its antagonistic relationship with the west, wasn't as clearly understood or recognised in 1945. Information about many pre-war atrocities like the Holodomor were suppressed, while the chaos and horror of the Nazis advance camouflaged others, like the Katyn massacre. Consequently, there wasn't the same readily understood 'smoking gun' to provide a powerful causus belli for another total war.

Finally, and perhaps most importantly, the western allies were divided about how to navigate the post-war diplomatic world. Some politicians like Churchill did see the advance of the USSR across Eastern Europe as an inevitable existential threat, and had tried to make extensive plans to minimise their advances, such as by landing Western troops in the Balkans to take them of Soviet forces in the east. He'd even masterminded Operation Unthinkable, a plan for a continuation war against the USSR.

However, that understanding of the Soviets and democratic allies as being inevitably ideologically divided was not subscribed to by everyone in 1945. In particular, some Americans leaders, including President Trueman, saw the UK and France as direct geo-political rivals as much, or more, than the soviets might be. While the USSR might be run on a different political and economic system, the highly-industrialised maritime trade-based economies of the other western allies had been a more direct competitior to the US and its economy that the USSR had. With Britian and France exhausted and broken from the war, some saw it as an ideal oppotunity for the US to surpass them as world and economic leaders, prioritising that over their ideological differences to the USSR.

Finally, I think it's important to remember how costly another war against the USSR would have been, in terms of both men and material, and just how economically shattered all the allies bar the US were by wars end. Already Britian would have to continue rationing food until 1953, and all the allies would face a decade or more of economic depression and crisis as a result of the war. Had they had to continue to fight an even more costly war, that economic damage would have been much more severe.

So with the western allies divided, their populations war-weary, and the USSR not yet widely accepted as an inherently antagonistic due to her ideological differences, mustering support for a war that would make defeating the Nazis look like a cake walk was politically impossible, regardless of whether they had the military or economic power to accomplish it.

Hope this helps

Have a spectacular day