Surly there were some pretenders to the Byzantine throne kicking about 400 years after the fall of Constantinople? Or if lacking that, why didn't they just turn to a prominent Greek family and ask them to be king?
I mean, of all people to pick as your first king, they pick Otto, who doesn't speak Greek and who is the wrong religion. And not only that, but a minor at the time! He couldn't even be actual king for a few years.
Is there some Realpolitik that I am missing here?
Actually, there weren't any Greek pretenders to the Byzantine throne. The last of the Palaiologos with a claim, sold his rights in the 15th century to the French King, the Spanish King, and lastly to the Ottoman Sultan.
There were, and still are, several descendants of the important Byzantine families at the time. Many of them were leaders of the revolution and had themselves positions of power either at the Sublime Porte or were princes of provinces such as Wallachia. The problem with all these powerful families, whether of ancient stock or more recent, was that they all hated each other and didn't trust each other. Add to that the fact that major political forces in Greece at the time were the "Russian Party", the "French Party", and the "English Party" with each of those major powers vying for influence in the Turkish underbelly you get an idea of the context of the time.
Each of these parties wanted someone from their respective sponsor countries to donate a prince to take over or have a sort of personal union but the others wouldn't permit it. This is why the major powers settled on a prince from a "safe" country.