Because of the claimed equality between federal regions, the ones that until 1918 had royal status (Bayern, Saxony, and Wurttemberg) would not be acknowledged as Kingdoms. But the heirs of such royal houses would see their title restored, and so for the lesser ranks, albeit of course not being anymore the rulers of their own regions. At the same time the Kaiser could have the right through parliamentary approval to appoint new nobles or demote others or even strip their titles. The nation would compensate the noble families victim of acknowledged Nazi purges (one of the most renown cases being Maurice of Hesse, son of Philip, restored in all his dignity despite being at the time more a Prince of Italy than of Germany). But the discussion between returned private properties and ones retained by the German state would cause certain legal contentions – one of the most famous being the property of the castles built by Ludwig II of Bayern, with the Wittelsbach determined to get their palaces back versus the federal state of Bayern. The legal cause lasted for decades and ended in a compromise where the Wittlesbach would obtain a limited property and use and a percentage of the profits coming from touristic visits.
Why not a make the 'fourth reich' more like the first by adding a rotational system like in Malaysia or an elective system which allows the people to select the heir to the throne from amongst the old royal families? That would be a decent compromise between the monarchist and the republican factions in and of itself, and also be a good justification for the Kaiser retaining real power.
The Crown Prince shouldn't have nominally a territory of Germany (see Prince of Wales) and then which one, as Brandenburg and Prussia were not viable choices? Also what to do of the daughters of his older brother, if the Prussian title went less? And the Kaiser won't likely dare in the first years of his reign to concede titles over his family to not let show the Germans to take already advantage of his newfound status... In short the nobility issue would give to Louis Ferdinand and also Adenauer some headaches for a while.
Prussia had plenty of provinces in the west by the time the first world war occurred. The most prestigious of them was Hanover, the use of which would be a diplomatic insult to the British. However, making junior Hohenzollerns princes of Westphalia should not be challenged by anyone. In the above-proposed elective system, this would be their fallback title should they lose the title of Kaiser.