They did so for two reasons:
1. To get support from certain princes which would make them (Hitler, Goebbels etc) more socially acceptable among the upper echelons of society;
2. They were keen to get the support of the military and conservative fractions of society, both fractions (like the Prussian junkers) wanted a restoration of the monarchy and the old social structure above almost everything else.
Now it is highly unlikely that once into power, Hitler seriously contemplated a restoration of the monarchy. But by flaunting the idea prior to 1933 and in his early years as Reichskanzler, he was able to secure the support from groups within society who all fell for it.
That a Prince of Hessen was contemplated (or at least mentioned as a candidate) should not surprise anyone; the four Hessen-brothers were firm nazi-supporters almost from the very beginning.
I can highly recommend the book Royals and the Reich on the issue. And as a counter-balance also the book 'The Palace and the Bunker' about royal and noble resistance against Hitler's Third Reich.
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