Problem with that was the international situation. As I recall there was a Hapsburg regent in Hungary briefly - I think he resigned as armies started marching towards Budapest.Hapsburg on a throne of one of the successor states is possible. In theory Hungary was still a monarchy until end of WW2 with a regency. Maybe dice break differently when Karl tries to keep his throne as King of Hungary.
Michael
It is difficult for Hungary to restore the monarchy without that being seeing as a provocation by her neighbors.
I think it is because so many Weimar leaders, including both of their presidents, were royalists. If the Kaiser had just lead a cavalry charge on a machine gun post as so many wanted, well imagine what may have happened there....I am baffled as to why most people voted the Kaiser, when the Ottoman Sultan actually did survive the war and wasn't abolished until 1924.
(I'm not sure about the political views of the acting presidents)
Additionally, the Sultanate was abolished in 1922 (although it did take them another year to get a republican constitution in place). I suspect you are thinking about the caliphate, which is a different issue. I mean, if the British monarchy were overthrown and the Queen remained Supreme Governor of the Church of England for a few years that wouldn't mean she was still a reigning monarch.