AHC: Wittelsbach Germany

With a post WWI PoD, could the monarchy get restored in Germany (constitutional, or otherwise) with a Wittelsbach dynasty instead of Hohenzollern?
 
Why should Prussia (more than 60% of the population of Germany) accept a catholic bavarian king/emperor?
Who should govern Prussia, if the king/emperor is at the same time king of Bavaria?
If there are still some Hohenzollern alive, the conservatives and monarchists (DVP, DNVP) would support them. I don't see any support for Wittelsbach outside Bavaria. But a Hohenzollern restauration is possible (but difficult) in Weimar Germany. After WW2 a monarchy in Germany is nearly impossible.
 
Why should Prussia (more than 60% of the population of Germany) accept a catholic bavarian king/emperor?
Who should govern Prussia, if the king/emperor is at the same time king of Bavaria?
If there are still some Hohenzollern alive, the conservatives and monarchists (DVP, DNVP) would support them. I don't see any support for Wittelsbach outside Bavaria. But a Hohenzollern restauration is possible (but difficult) in Weimar Germany. After WW2 a monarchy in Germany is nearly impossible.
Just more ethnic cleansing post war.
 
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