Prussia had been for all of recent memory at this point a thorn in the side of Europe. I can't give you an answer about why the Allies dismantled Prussian politics as that's about 20 years out of my wheelhouse but I can give you some much needed context. Let's wheel it back to the year of 1814 when the Congress of Vienna would begin to redraw Europe after Napoleon's defeat. After 25 years of constant war and destabilizing revolts, conquests, and betrayals the big players of Europe wanted to create a Europe in which the power would be shared. A delicate balance of power where no side would be strong enough to take on everyone else.

It would work for the most part. Outside of revolts, Europe would not experience inter-war until 1848 -- when Prussia would invade Denmark for German Holstein. Prussia and Austria would then go to war over control of the German minor states that were freed by the Congress of Vienna, creating what is referred to as the "North German Federation." Then in 1870 Prussia would through guile and political savvy goad France into declaring war on them -- the result being Prussia annexing Alsace-Lorraine, bringing the Bavarian and Württembergers closer to the German "identity" and, with this newfound pan-German unity, declaring a unified German state.

I hope you're seeing a pattern here. Prussia is commonly referred to as, originally by a Prussian Friedrich von Schrötter hilariously enough, "not a country with an army, but an army with a country." Prussian militarism and the need for expansion is directly responsible for breaking that delicate balance of power in post-Napoleonic Europe. It was bound to be broken eventually one could say but Prussia was certainly the one to do it through an explicitly expansionist motive. Through this expansionism would come the formation of a German state who would overnight become a world power and within a decade become the most industrialized nation on Earth.

Despite being technically a Federation with Prussia, Bavaria, Württemberg and Saxony as the major players, Prussia would be the dominant political and military party. Its militaristic history would dominate politics up to and throughout WWI. Prussian nobles and generals were given precedence for respect and reinforcements and training and supplies in WWI and were seen as "greater". You could create a well cited, well reasoned argument that the culture of Prussia, which was inherently militaristic and based around the superior German people, would birth the concept of Weltpolitik -- the policy of world domination through aggressive politics and overseas expansion -- which can be directly attributed to the rising tensions of 20th century Europe and that infamous "powder keg" analogy we all learn about.

I honestly don't know precisely why the Allied commanders personally wanted to destroy the political entity of Prussia and the culture of Prussia. It's completely out of my area of study and I have no primary sources there. However, the concept of Prussia is well within my area so I feel confident in applying that just a couple years later. I have no issue making the assertion that after a second World War started by an aggressive, expansionist Germany the Allies (and former Entente) were sick of the militaristic culture of Germany which happened to stem from Prussian culture, history, and politics. Post-war treatment of Germany was heavy handed and to make sure they were never going to do what they did a third time. That includes the massive denazification campaign we all know about and demilitarizing the populace by striking at the heart of its militaristic culture -- Prussia.

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Notes:

Mosse, W.E., European Powers and the German Question

Carr, William, The Wars of German Unification

Strachan, Hew, The First World War: To Arms