I visited the Buchenwald concentration camp last week and in the exhibition they had a fairly big part dedicated to the administration of the camp, along with its bureaucratic procedures.
I asked our tour guide about it and he explained that in the context of the concentration camps having a big administration was useful so tasks could be split up easily and responsibility was loaded on many different shoulders. For example that SS soldiers were "only" responsible for registering prisoners' names and taking their personal belongings while they had no responsibility with bringing them to work or other tasks.
This was supposed to also be a tool to keep up the SS soldiers' attitude so that they were only responsible for one part of the cruelty but not all of the cruelty that was brought upon the prisoners.
That made me wonder, in what other ways the Nazis used their bureaucratic system to maintain stability and keep everybody in line and also if the horrors of the 3rd Reich would have been equally possible with a less sophisticated administrative system?
And as a follow up question maybe:
Did many SS soldiers and other Nazi officials refer to the administrative system as a form of excuse for their involvement in the crimes of the war and Holocaust afterwards?
Evidence suggests that the administrative system behind the Nazis was much less sophisticated than apparent. In fact, many of the downfalls of the Third Reich are based upon a split in administration in all aspects. For instance, the SD (Sicherheitsdienst: Nazi Intelligence; a branch of the SS) was almost completely separate and did not agree with Abwehr (German Intelligence).
The problem is that both exist at the same time and do not work together. The German Intelligence was not for the planning and execution of the Holocaust. Many of the reasons included the ideas that ammunition and resources should be used for the war effort. Many of the German intelligence's higher officers were not fond of Hitler nor his beliefs.
Even 'The Last Solution to the Jewish Question' saw many changes through the Third Reich's time period. The original plan was to move the Jewish population to Madagascar.
For your question on whether it would be possible with a different system: That question can only be answered with an ahistorical response - if it had not happened, us historians cannot GUESS as to what is possible.
If you wish to compare different administrative systems with mass executions in a similar time period, look towards Stalin's Great Purge of 1937 - 1938.