I’ve made a study of the period so hope I can add a few things along with Loach’s salient points.
At Stalingrad, Hitler promoted Paulus to Field Marshall. It was a not so subtle hint that he should commit suicide, immolate himself along with the Sixth Army rather than capitulate. When he found out that he Paulus had instead surrendered to the Soviets he was furious. It had spoiled the heroic narrative. Likewise in Berlin he viewed his own death as part of his ‘great man’ mythos to inspire future National Socialists. He dictated just before his date with a burning ditch;
“From the sacrifice of our soldiers and from my own unity with them unto death, will in any case spring up in the history of Germany, the seed of a radiant renaissance of the National-Socialist movement and thus of the realization of a true community of nations.”
The OSS compiled a psychological report on Hitler during the war and included predictions on his likely fates, stating that suicide was the most likely.
*This [suicide] is the most plausible outcome. Not only has he frequently threatened to commit suicide, but from what we know of his psychology it is the most likely possibility… He knows how to bind the people to him and if he cannot have the bond in life he will certainly do his utmost to achieve it in death. He might even engage some other fanatic to do the final killing at his orders.
Hitler has already envisaged a death of this kind, for he has said to Rauschning:
“Yes, in the hour of supreme peril I must sacrifice myself for the people.” *
As for why he didn’t go out fighting, although he was no physical coward (he was a runner in WWI, an extremely dangerous task) as well as being a decrepit shell of himself by the war’s end his bigger fear was being wounded, captured and paraded around in a cage. To avoid this ultimate humiliation he decided against any direct contact with the enemy. The OSS opined that the possibility was not unlikely and extremely undesirable from our view;
*"Hitler might get killed in battle.
This is a real possibility. When he is convinced that he cannot win, he may lead his troops into battle and expose himself as the fearless [Page 245] and fanatical leader. This would be most undesirable from our point of view because his death would serve as an example to his followers to fight on with fanatical, death-defying determination to the bitter end. This would be what Hitler would want for he has predicted that:
"We shall not capitulate...no, never. We my be destroyed, but if we are, we shall drag a world with us...a world in flames." .
"But even if we could not conquer them, we should drag half the world into destruction with us and leave no one to triumph over Germany. There will not be another 1918." *
As for why he didn’t just flee. The last sentence of the previous paragraph says it all; there would not be another 1918. To say Hitler was obsessed with the end of World War One is putting it mildly, it went hand in hand with his hatred of Jews in defining his political career. The Novemberverbrecher, November Criminals, he believed had betrayed Germany in 1918, sold out her soldiers, made a mockery of battlefield sacrifice. In Mein Kampf he wrote;
*"Was there no obligation toward our own history? Were we still worthy to relate the glory of the past to ourselves? And how could this deed be justified to future generations?
Miserable and degenerate criminals!
The more I tried to achieve clarity on the monstrous event in this hour, the more the shame of indignation and disgrace burned my brow. What was all the pain in my eyes compared to this misery?"*
In other words to be seen in German history alongside those who had stabbed her in the back in 1918 was, literally, a fate worse than death.