[Sharkû]

I have to say, I find your analysis of his pride as Denethor’s decisive fault a bit reductive, Underhillo. While it essentially is of course not wrong, I hold against it the fact that Denethor’s pride and arrogance were not always the main, and arguably never the sole reason for those of his reactions which can be judged as imprudent from the lofty seat of literary or historical criticism (this is in my humble opinion also one major flaw of, for example, Sallust – personality and character are rarely the only, albeit of course often an important, motivating force of history; and it has to be noted that this is almost never realized during the life-time of a person).
The situation with Pippin and the ‘tool of other men’s purposes’ –quote may reveal his pride, but still do not lessen the prudence behind Denethor’s action, respectively his sentence. Now, that he mistrusted Mithrandir that much, was of course a result of his pride, and can – though only with hindsight! – be considered a mistake.
“Denethor is clearly more committed to maintaining his pride than he is even to the defense of his realm.” I have to differ here. His own sake and the sake of Gondor were inevitably tied, and even if his own salus had been more important to him – what I still doubt –, an action for the one would also further the cause of the other. What the incession to act was in first place may be more interesting to a psychologist, but I will not go there.
His overly developed self-confidence led him to face Sauron and to dare to have the resolve to take the Ring (purely hypothetical, though), but was this too wrong? Denethor was no master of Ring-lore (something I will elaborate on further down when we come to the fascinating comparison you made, Undé); one could not demand of him to know the facts that the Ring was not to be mastered by man. And one man who could have achieved it, had it been possible, would certainly have been the wise steward.
Conclusively for that aspect, I may say that although Denethor’s pride was inherent, it was not, at least not the only thing, what made him fall; unlike the proverb.

As for your analogy of the methods of leading used by Hitler and Denethor, it is certainly bold, but intriguingly fitting, and precise even to some details.
I will simply add some points as I notice and see fit. Hitler was notorious to reject any counsels for much the same reasons as Denethor (see my previous posts for the latter), experience/skills and descent (although with Hitler it was more the case that he despised those of noble origin among the conservative generals et alii, not the simple men). As a cause, it of course also was the other way round with the World War private.
Denethor wanted the West to perish as the consequence of his failure, and no longer being worthy of a place among the people of Middle-Earth – Hitler said the same about the German people.
Now, Hitler of course never had a line of ruling forebears, nor did he ever intent of founding one himself (speculative biological obstacles aside). Both leaders, however, abandoned the logical dichotomy of leader and people, both viewed the latter as being vitally dependent from the first, as you mentioned quite well.
Could the good relation to Boromir, as his identical image of an apprentice, echo the relation of Hitler and his apprentices in the party, most of all maybe Rudolf Hess? While this very comparison probably goes to far, the way they choose their familiars was similar for both. Neither valued counsel, but rather kept their minions in mutual competition. And since the own judgement was the best anyway, such counselors as they chose were apprentices which could be used as their right arm in some affairs where others were not to be trusted (the mission to Imladris, for example, or the armaments industry Hitler gave Speer the command over).
Hauntingly striking appears to me the mistake of both leaders to overestimate their own competence in vital fields where they were actually far behind the learned and wise. For Denethor, this was Ring- and Elven-lore; for Hitler, the whole field of military strategy. This was eventually were both failed, too.

Now, is this not the sign of arrogance and pride, and was it hence not the ultimate cause for their demise? As I said, this cannot be rebuked totally. Instead, I propose an approach that takes the respective circumstances more into account, for historical events are never isolated, and therefore the characters of leaders can never be a sole cause for either good or bad. At least with Denethor, this very flaw we are discussing would not have been his demise in any other situation but the crucial War of the Ring, and, even the way it was, his actions never led to the actual end of his realm, nor would he have had the potency to cause that, I argue. Minas Tirith would have continued to fight without Denethor, even if the leaders who took his place were of lesser stand or had been more open to debate than Mithrandir, Imrahil and Elessar.
Of course, here the time of Hitler was totally different, the war was lost before April 30, 1945. And the Führer indeed was the main cause both for its beginning and the defeat of his own side.