Albert Speer (Hitler’s architect and eventually somewhat of a friend) often wondered this himself and came to the conclusion that Hitler’s mind and personality seemed to work more like that of an artist and therefore embraced the night as a sort of ‘creative’ stimulant.
He described this in his book “Inside the Third Reich”. He mentioned Hitler to be somewhat more free minded in his personal ways, with occasional intense outbursts of energy where he would have beyond excellent focus/thinking (brilliant even), then followed by (usually) longer periods of downtime where his thinking was more clouded.
A strong repetitive 'regular' schedule especially where bedtimes are concerned was also therefore not something Hitler considered to be a necessity, rather the other way around. He preferred to stay up late with his guests. He loved the nighttime. Even though he was no drinker or smoker.
And then of course there were the endless late night repetitive speeches (monologues really, same show several days a week) he gave his surrounding guests at his Berghof mansion. I personally suppose that, in a way, he was really contemplating his own mind and thoughts over and over again at these times. Sometimes literally whilst pacing up and down the room. And being the Führer of course no one would interrupt him but instead would listen to the same story/thoughts/theory/philosophy over and over again.
Hitler always saw himself more as an artist than a politician. Even after his failed career as a painter. Even after becoming the Führer.
This reasoning to his continuously staying up late, albeit rather vague to many perhaps, makes sense to me as I guess it did to Speer.
Fun fact: Hitler was also known to have somewhat of a morning mood. Which was one of the main reasons they did not dare wake him even though allied troops had broken through the Atlantic defenses and were entering Normandy. He was the only one who could authorize two nearby highly trained special SS Panzer divisions to move. Which were stationed there specifically to prevent an Allied invasion. But Hitler only trusted himself with the authority to move them. Never perhaps in history did sleep come so costly.
In addition: I’m also pretty sure the methamphetamine shots his physician Theodore Morell eventually provided him with can't have made an improvement to his bedtimes or his morning grogginess. However, Hitler was already known to stay up late before he met Morell.
