3 answers. Efficiency. Genealogy. Property.

The entry logs at Dachau and Mauthausen are very specific and brief. They include the new inmates name with assigned corresponding serial number, DoB, place of origin. Sometimes they would add notations later that would specify if they were released or dead. But considering the scale of the holocaust, going back through a chronological and alphabetized list to find a name in order to specify whether the inmate was deceased or released was simply not efficient, or logical. Most likely they were dead or in a labor camp on their way to death.

Efficiency

With this limited data the Nazi’s were using it to create a sort of back end database. On the front end they had been compiling the lists of Jews which were demanded from and provided by the towns, regions, synagogues, schools, police and the friendly neighbors. These lists became necessary to determine the size of the forces needed to round everyone up at once, unannounced , and evacuate them with trains. In order to apply an overwhelming force you must first determine the size required to accomplish your goal. You need to know how many train cars you need, and at what time it should arrive and depart.

By comparing your front end list to your back end lists you can determine the efficacy of your units, the company, the squads, the trains... You can tweak your execution of process and tailor make each attack to fit your needs. Maybe there are only 100 people you need to find in a rural area... it’s easier to execute them than gather them and transport them to trains and so on. Maybe you need 2000 troops with dogs, tanks and road blocks to gather 10000 people up.

You also had tens of thousands of interrogations going on at a local level. For example, one neighbor or one Hitler youth would make a report about a family of Jews or Gypsies that they knew about. That report would be followed up and investigated. If an arrest was made there was a record of it, including the sentence handed down. When that prisoner was transferred to the camps there were corresponding intake records. This will become relevant later.

Genealogy

The Nazi’s at first had different classification of Jews. Whether you were 1/2 Jew or 1/8 Jew, if your mother a Jew or your maternal grandfather. Overtime they made it easier and easier for people to be classified as Jews by lowering the requirements and widening the definition.

At first they made the Jews register as such and describe exactly “how Jewish” they were by having them include who exactly was Jewish in their ancestry. They were assigned a ratio of how Jewish they were and if it exceeded that amount they were considered “undesirables”. Eventually the Nazi’s settled on the qualification of being Jewish if you had 3 grandparents who were Jewish. At this point you would lose your citizenship, legal rights, education rights and labor rights. In order for this type of law to be enforceable you need lists of names and the appropriate files and data to give or revoke rights, citizenship, create deportations or imprisonment.

On the front end - the compilation of these lists was necessary in order to determine whom was related to whom. To trace back who your parents are, their parents and their parents. They can see and visualize your siblings and their children on charts and maps. All of this quantifiable data was created with the goal of eliminating all non Arians from Germany, but first creating a slave army.

Property

This was the long game of the Nazi’s. They never made it this far so people tend to overlook this in the same manner that people tend to overlook the plans Hitler made for occupying Russia and the USA. Property that was seized from the people who were imprisoned has no calculable value because it can’t be counted. There are answers that vary wildly but simply using common sense puts the number in the low billions of 1938-1945 money. Consider the number of known people killed, their homes, cars, horses, jewelry, farms, businesses... A transfer of wealth that large requires a paper trail even larger to make things legal. And the Nazi’s went through great pains to make the atrocities they committed legal, step by step. How do you legally “give” a 10,000 square foot mansion to a General when the legal owner of the deed and his next of kin is deceased? How do you transfer a business from one entity to another? How do you seize bank accounts from international banks? If you change the laws to make everything legal, you don’t need to hide your data. There is nothing to hide.

So, why keep the incriminating records? Because they were not incriminating. They were never supposed to be seen because they were supposed to win the war. And the war was against the world. There would be no country on earth left to do anything about it. Not Russia, the US, England...

At the end of the war in 1945 the Nazi’s scrambled to destroy all the evidence. Including paper trials and the human survivors who could testify.

Many of the records discovered by the allies were compiled and used to prosecute war criminals. However, Germany released an 11 million page dump in 2006 that got overlooked. Some of it is accessible here.

Edit - This answer was made specifically pertaining to “why did they keep records of each individual killed” . But even more specifically, the Nazi’s didn’t. The “aristocracy” of the Nazi’s tried to... they tried to implement systems and records of each individual but ultimately they fell short of this goal. The boots on the ground who carried out the commanders orders are responsible for hundred of thousands, if not millions, of murders. Murders committed for many purposes, but never reported or recorded. Never mind the mass killings of Russians by the Nazi’s AND the Russians during the push east to Moscow. Entire towns and cities were destroyed with little warning, if any at all. Those peoples names were not recorded, but lost in time. We will never truly know how many people died in WW2. The estimates are from 50 million to 100 million people, including soldiers on all fronts and civilians. That is a gap of 50 million people. We will never know.

u/commiespaceinvader wrote a great answer on this.

In addition to the more specific answer posted by /u/cckerberos, there are several answers by /u/commiespaceinvader which touch on the reasoning behind the Nazi bureaucracy. Firstly, their answer to What distinguished the Holocaust from other genocides in history? points out that the use of bureaucracy and the other tools of the modern state was the distinctive thing about Nazi killings compared to other genocides. Their answer to How did Hitler manage to subvert the court system in Nazi Germany? expands upon how the Nazis subverted a pre-existing legal system in order to get a patina of legality on their actions. Finally, their answer to Is it fair to say that Nazi Germany applied the logic and actions of colonialism to European people? compares the Nazi state and its treatment of disfavoured social groups like Jews and Sinti to the bureaucracy of European colonialism. More can definitely be said on this specific question, but hopefully, between those answers, you should get something of a sense of the historical factors that went into Nazi bureaucracy.