This idea rests on several misconceptions and misunderstanding of what the Nazis were and thought. It assumes a homo economicus model, i.e. that people will always act in a way that is most rational, economical etc. and that this remains the same in every historical society unperturbed by ideology, discourse, and believe-systems. For the Nazis, these camps as well as the Holocaust did exactly what they wanted to achieve and what they regarded as integral part of their war effort and they did at comparatively low cost and even profit. And secondly, it overlooks the importance of the camps and camp labor system within the German war economy. One reasons why Germany was able at all to fight for as long as it did were these camps.

In order to be able to go more in-depth here, it is important to differentiate between Death Camps and Concentration Camps. Death Camps were the camps of the Aktion Reinhard -- Sobibor, Treblinka, and Belzec -- as well as the Chlemno Camp with Auschwitz and to a certain degree Majdanek serving as both Death and Concentration Camps.

What sets apart Death Camps from Concentration Camps is that Death Camps were indeed what the name suggested, a camp to kill people. In those camps, about 1.5 million people were deported to and the vast majority (like 99%) killed immediately upon arrival by being herded into gas chambers. Aside from those who did work for the guards and camp administration as jewelers, cobblers and so on and those in charge of emptying the gas chambers after the people inside had been gassed, all the people deported there were immediately killed and even those workers were killed in regular intervals.

What is important to understand here, is that the Nazis did view this as necessary to their ongoing war. They understood their war not just as a war for political or military but also for racial dominance. I go into this here, here, and here but in essence the ideological delusion that the Nazis that they were fighting a war with the Jews, lead them to killing them as an essential part of the war effort. For the Nazis Jews were a security concern and every Jew under their rule was an additional security risk. Therefore, occupying Poland with its approx. 3 million Jews really put the pressure on the Nazi leadership to find a solution to this purported problem. And later when the war against the Soviet Union started the Barbarossa and Einsatzgruppen decree made it an essential part of this "war of ideologies" as the Nazis dubbed it, that the Jews had to die because the Jews were an essential threat that was potentially everywhere. "Where there is the Jew is the Partisan and where the Partisan is, is the Jew", the logic ran within the Nazi leadership. To understand the Holocaust and the Nazis' policies it is tantamount to realize that every Jew was a potential thread and by the time the war started against the Soviet Union and thereby got really serious for the Nazis, every Jew everywhere became a potential security risk. Thus their policy escalated into killing them and once they started that, killing them became as essential to the war effort in their mind as food supplies, logistics, and the advance of Army Group Center.

Similarly, the Holocaust also had an important economic side, as I elaborate here and here. First of all, certain economic factors were driving forces, at least in speeding up the killing process. According to historian Christian Gerlach, Aktion Reinhard, the killing of over a million mostly Polish Jews, occurred earlier than originally envisioned by the Nazis because of the German Food Situation. Killing a large number of people means you don't have to feed them and the killing of the Polish Jews started right when Nazi Germany would otherwise have been forced to cut back rations for its own population -- something the Nazis wanted to avoid at all costs because of their experience of WWI where food shortages had been a major factor in Germany having to agree to an armistice in 1918.

Similarly, once the Holocaust was underway, it was a profitable venture. It virtually paid for itself. As I tried to show in one of the answers linked above, the total value of Jewish assets seized by the Nazis in today's money would be some $143-$215 billion. And that doesn't even take into account the profit from slave labor of camp inmates before they were gassed in Auschwitz or Majdanek as well as the use of their labor force in the Ghettos before they were even sent to the camp. The Holocaust was a venture that wrote black numbers and contributed massively to the German war effort.

Which leads to the Concentration Camps: Concentration Camps had been a defining feature of Nazi rule since its very beginning in 1933. Serving as camps for political opponents and other people the Nazis wanted to see imprisoned, they subsequently took on an important economic role in addition to their role essential to German security. The SS ran companies like Deutsche Erd- und Steinwerke (German Earth and Stone Works) solely on labor from the camps and supplied virtually all railroads in occupied Europe with the gravel to go under the tracks. Oswald Pohl of the SS's Economic and Adminsitration Main Office (Wirtschafts- und Verwaltungshauptamt, WVHA) estimated in 1941 that a Concentration Camp inmate would bring in a profit of 1629 RM when doing forced labor in a camp for nine months. This included not only the income from renting them to companies but also "assets" such as his gold teeth etc.

During the war these camps were essential tools not only in serving as prisons for people the Nazis regarded as political opponents and security risks but also as a major source of labor for large German companies. The SS "rented" Concentration Camp inmates to large companies for 0.2 RM a day and in some cases, such as with the Buna Works at AUschwitz-Monowitz, even build the IG Farben comapny their own Cocnentration Camp right next to their factors. Concentration Camp labor was not a drain on resources but absolutely essential to maintain the German war effort from 1942 onward with so many men at the front at dead.

In this sense, the camps and the Holocaust were pretty nifty things in the eyes of the Nazis. They fulfilled essential security functions, were a profitable venture, and an integral part of the war effort.

The narrative of the camps as a resource drain is one often pushed by people who like to pursue the narrative of "ah, if only it handn't been for the Holocaust, the German Army in all its glory could have won" while wishing for such a victory. This narrative completely misrepresents / misunderstands the Nazis, their ideology, and their war. The war of the Nazis is unlike WWI not a war of political domination, it was a war that was as much about race, living space, colonial pipe dreams and ideology than it was about political dominance. The war against the Soviet Union was always envisioned as a war of annihilation, including large swaths of the Soviet population. The war of the Nazis is not separable from the Holocaust and the Camp System, in the way it was planned and in the way it was carried out.

Sources:

• Adam Tooze: The Wages of Destruction: The Making and Breaking of the Nazi Economy, London 2006.

• Karin Orth: Das System der nationalsozialistischen Konzentrationslager. Eine politische Organisationsgeschichte, Hamburg 1999.

• Nicholaus Wachsmann: KL. A History of the Nazi Concentration Camps.

• Christian Gerlach: Krieg, Ernährung, Völkermord. Forschungen zur deutschen Vernichtungspolitik im Zweiten Weltkrieg. Hamburg 1998.

• Götz Aly, Susanne Heim: Architects of Annihilation: Auschwitz and the logic of destruction, Princeton, NJ: Princeton University Press, 2002.

• Richard Evans' Third Reich Triology.