Do you think the German monarchy could've fallen at some point? Maybe if Prussia had united the little states instead of Saxony? Perhaps the country would've been a bit more Catholic too. I wonder if Hanover or Westphalia would've been absorbed by Prussia. Maybe even Magdeburg-Anhalt could have become a Prussian state, like "Saxony-Anhalt" or something. If the monarchy fell, maybe Posen, Silesia, East and West Prussia, and Brandenburg might still be considered provinces of a 'Free State of Prussia', trying to cling to the past for some semblance of normalcy, rather than breaking apart into states in the 20th century.
Maybe if Prince Wilhelm hadn't died and had become Kaiser instead of Prince Henry, that could help get it done?
I was reading about the Kaisers, going from Heinrich I to his eldest, Wilhelm II, his brother Wilhelm III, then Alfred I, and finally to Barbara I (how long did it take to get Salic law overturned??), and the current Kaiserin, Edwina I. It kind of reminds me of Britain a bit, given all the family relations to the Saxe-Gotha royal family and all.