Yeah. Anyone who thinks that the Nazis were leftists is fooling themselves.
Most of this stuff was still strictly hierarchical; the Hitler Youth, for example, was pretty explicitly a prep school for military service, in which the superiority of officers over enlisted men and of senior officers over junior officers is pretty iron-clad. Part of the function of the Hitler Youth was to talent-scout "officer material" kids and place them in leadership positions. It represented a break with traditional aristocratic hierarchies, but only insofar as it substituted them for the hierarchy built through competition.
To build off of this, the Nazi adoption of the
Führerprinzip was intended explicitly to synergize with the fundamentally paternalistic expectations of the German officer corps. In 1934, at the tail end of the
Machtergreifung, the
Reichswehr published its new officers' leadership manual,
Truppenführung. The manual and its emphasis on the leadership principle (among many other things, of course) were not
conditioned by the new Nazi leadership. They were old-school German military notions, and the Nazi espousal of the same basic ideas was a happy marriage of the minds.
A hierarchy built on competition is about as opposed to a hierarchy based on ancestry as you can be unless you ditch hierarchy altogether.
Hitler used and worked with the traditional hierarchies, but he was contemptuous of them and his policies undermined them (eg massive expansion of German army undermined the aristocratic traditional officer corp)
The only hierarchy he really cared about was racial.
The massive expansion of the German Army undermined the aristocratic officer corps to an extent, but
contra Craig (who in general overstates political grounds for anything occurring in the Prussian-German military) there are a decent amount of modern arguments suggesting that that work had already been done by the experience of the First World War.
Reichswehr officers saw how cumbersome the system got with OHL and the Military Cabinet attempting to suppress "mustang" NCOs from becoming officers (expansion of the grade of
Offizierstellvertreter, etc.) and knew that in order to expand the army enough to win the next war a lot of the social inflexibility of the
Kaiserreich would have to be abandoned. The
Reichswehr was explicitly designed as a cadre force from its inception, with the understanding that private soldiers, NCOs, and lieutenants would become field-grade officers in the "next war".
Thus, while there was still inevitably some pushback to Hitler's expansionary policies from the higher officers of the early
Wehrmacht, and while some of that
was due to concerns about the social dilution of the quality of German officership, the majority of the resistance actually came on
technical grounds. Most German officers understood the need to vastly expand the army and thus the officer corps, but thought that their
military quality was being diluted by how rapidly the new divisions were created, not necessarily their
social quality. New formations came on line without even a shred of the full TO&E. The old
Reichswehr personnel didn't suffice to provide training cadres for the new thirty-six division force, so training quality was lower. Germany did not end up getting the time to fix these problems before the outbreak of the war, so the
Wehrmacht reluctantly acknowledged that their divisions necessarily had a high amount of variation in quality, with the low-numbered formations of the early
Wellen ("waves") and the mobile troops at the top of the pyramid and the rest of the leg infantry closer to the bottom. This was a
tremendous change from the First World War, which Germany entered possessing a relatively uniform first-line army: every regular division was equivalent in quality (and that quality was
very high) and even the reserve divisions primarily differed from the regular forces in terms of available
equipment, not troop training. The
Wehrmacht's new set of circumstances took adjustment, but it was much more of an adjustment due to military efficiency concerns, not
primarily to social hierarchy ones.
Meanwhile, the new military hierarchies that were created in the SS often drew from the members of the old. Himmler and his minions explicitly courted the old
Adel on their estates, and had a decent success rate in attracting them to the SS's ranks. Professional men made up another large proportion of SS membership, and could expect to advance further in the organization than the poorer thugs who only counted brutality, bigotry, and the right genes to their name. And while the SS might have been rather more willing to recruit from lower classes than had the old imperial officer corps, it explicitly promised to make these men and their families into the new nobility of the
Reich. An SS academy was called a
Junkerschule, drawing direct and blatant parallels to the nobility of old, and its curriculum owed a great deal to the old military-school routine. It's hard to find much egalitarianism in the whole setup. Sure, "new men" were recruited into the ruling hierarchy, and some "old men" were kicked out - but that's been true of all sorts of deeply hierarchical regimes throughout history. A king making his drinking and whoring buddies into nobles didn't make his feudal monarchy more "egalitarian".
It's true that some of the "new men" of the
Waffen-SS clashed with the
Wehrmacht's leaders. It's even possible that disdain for their social standing influenced the problems. But it's frankly easier to see the widespread disdain of the likes of Sepp Dietrich, Felix Steiner, and Theodor Eicke as stemming from their limited competence as military officers, not
primarily from their lowborn station. (Steiner was not even lowborn; he had been an officer during the Great War.) When
Waffen-SS troops performed well, the
Wehrmacht was glad to have them around. When they didn't, the backbiting started.
I agree that Hitler generally opposed the old German officer corps and was willing to reluctantly use them for his own purposes. I just can't see that as
anti-hierarchical or
egalitarian in any real way because of the existence of the
Führerprinzip as one of the fundamental tenets of the Nazi movement. Even more than before, hierarchy assumed control of German lives - the Party ladder especially, from block leaders on up. And it's certainly not particularly
leftist to be willing to replace the old thugs in charge with a set of new thugs who are even
more in charge.