There is a variety of reasons for that, including some /u/kieslowskifan mentions in their post here on the killing of prisoners but one of the most important reasons is not so much to hide what they had done – the Allies were pretty well informed about that from 1941 onward – but to destroy the evidence that remained.

The Allies had made it clear from early on that one of their post-war priorities would be to criminally prosecute Nazi criminals. Already in January 1941 concerning the so-called declaration of St. James Palace, representatives from the Allied countries had expressed their determination to bring to justice those who committed crimes against the civilian population in occupied territories.

This intent was further underlined when already in 1942 the idea was floated to create a commission on war crimes that would be responsible for collecting evidence and setting up trials for those indicted and when subsequently 1943 not only saw the creation of this commission in form of the United Nations Commission for the Investigation of War Crimes and the first Soviet trials against Nazi criminals.

First, on the commission: Having been the product of several ideas floated especially by the governments in exile in London, specifically with Poland as a driving force behind the idea, it was set up in October of 1943 and should collect evidence, discuss questions of how to best organize prosecution as well as gather report from the members of the Allies about war crimes done in their country against their population.

Additionally in 1943 the first trial against Nazi war criminals took place in the Soviet Union in the form of the so-called Khrakov Trial. From 15-18 December 1943, the Military Tribunal of the 4th Ukrainian Front conducted the trial against the defendants Wilhelm Langheld, captain of the Abwehr with the 6th Army; Hans Ritz, SS-Untersturmführer in the Sonderkommando 4a; Reinhard Retzlaw, Senior Lance-Corporal of the German Secret Field Police; and Mikhail Bulanov, a local collaborator who had worked for the SK 4a as a driver, translator and general helper.The Khrakov Trial, which had been prepared by a Commission of the Soviet with a similar mandate to the UN War Crimes Commission (i.e. to gather evidence about German crimes perpetrated against Soviet citizens), ended in death sentences for all defendants and while the standards of evidence and justice at the trial can be considered lower to the later standards at the IMT in Nürnberg and various Western Courts, evidence for the crimes they had participated in was a key part of the trail itself.

This all goes to show that the Nazis, who had obviously heard about the trail and the commission were aware of these policies. Also in 1943 additional the Allies had held their Moscow Conference subsequent to which they published the following declaration:

The United Kingdom, the United States and the Soviet Union have received from many quarters evidence of atrocities, massacres and cold-blooded mass executions which are being perpetrated by the Hitlerite forces in many of the countries they have overrun and from which they are now being steadily expelled. The brutalities of Hitlerite domination are no new thing and all people or territories in their grip have suffered from the worst form of Government by terror. What is new is that many of these territories are now being redeemed by the advancing armies of the liberating Powers and that, in their desperation, the recoiling Hitlerite Huns are redoubling their ruthless cruelties. This is now evidenced with particular clearness by the monstrous crimes of the Hitlerites on the territory of the Soviet Union which is being liberated from the Hitlerites and on French and Italian territory.

Accordingly the aforesaid three Allied Powers, speaking in the interests of the 32 United Nations, hereby solemnly declare and give full warning of their declaration as follows: At the time of the granting of any armistice to any Government which may be set up in Germany, those German officers and men and members of the Nazi party who have been responsible for or have taken a consenting part in the above atrocities, massacres and executions will be sent back to the countries in which their abominable deeds were done in order that they may be judged and punished according to the laws of these liberated countries and of the Free Governments which will be erected therein.

This knowledge of being in danger of being persecuted lead to the Nazis introducing a policy of destroying evidence. When German forces started to be driven back by Allied Armies, particularly the Soviets, the Nazi leadership ordered the physical destruction of evidence. The main task of this fell to Paul Blobel and the Sonderkommando 1005. Starting to experiment on how to best get rid of the bodies of dead Jews, Blobel and his men started to exhume and cremate all the remains of the Jews shot by the Einsatzgruppen in May 1943 and continued to do so for many months.

It is also the reason, why the Nazis destroyed a wealth of documents held in various ministries and other agencies all across the Reich and why they destroyed concentration camps, including the crematoria at Auschwitz. They had an idea that the Allies knew about these things and that there were most likely going to be trials but in connection with those trials, their agenda was to destroy evidence that could be used in these venues against individual Nazis as well as against the system of Nazism itself.

Sources:

• Robert J. Hanyok: Eavesdropping on Hell: Historical Guide to Western Communications Intelligence and the Holocaust, 1939-1945, 2004.

• Witte, Peter; Tyas, Stephen (Winter 2001). "A New Document on the Deportation and Murder of Jews during "Einsatz Reinhardt" 1942". Holocaust and Genocide Studies. Oxford University Press. 15 (3).

• Jan-Erik Schulte: London war informiert. KZ-Expansion und Judenverfolgung. Entschlüsselte KZ-Stärkemeldungen vom Januar 1942 bis zum Januar 1943 in den britischen National Archives in Kew (Fundstück), in: Rüdiger Hachtmann u. Winfried Süß (Hrsg.), Hitlers Kommissare. Sondergewalten in der nationalsozialistischen Diktatur, Göttingen 2006 (Beiträge zur Geschichte des Nationalsozialismus, 22), S. 207-227.

• Arad, Yitzhak, Belzec, Sobibor, Treblinka, Indiana University Press, 1992

• Shmuel Spector, Aktion 1005 — effacing the murder of millions Oxford Journals, Holocaust and Genocide Studies. Volume 5, Issue 2. pp. 157–173.

• Joachim Neander: Vernichtung durch Evakuierung? Die Praxis der Auflösung der Lager – Fakten, Legenden und Mythen. In: Detlef Garbe, Carmen Lange (Hrsg.): Häftlinge zwischen Vernichtung und Befreiung. Bremen 2005,

• Karin Orth: Planungen und Befehle der SS-Führung zur Räumung des KZ-Systems. In: Detlef Garbe: Häftlinge zwischen Vernichtung und Befreiung. Die Auflösung des KZ Neuengamme und seiner Außenlager durch die SS im Frühjahr 1945. Bremen 2005

• Evans, Richard J. Lying About Hitler: History, Holocaust, and the David Irving Trial. New York: Basic Books, 2001.