But I wonder if that is truly so. What we know about the Daedric Princes is from the limited perspective of mortals. Perhaps there is more to the Princes, but they haven't been explored fully within the game. Lesser daedra have allegiances to various Princes, but there isn't much info about the culture of these daedra, their political systems, motives, etc when they are not on Nirn. Do they live in buildings? They seem to have ranks (Dremora, at least) in their military. What do Daedric Princes even do when they aren't paying attention to Nirn?
Well, the thing about Dremora is that they may be loyal to Dagon now, but like they said, "it was not always so." I think lesser Daedra, particularly the higher forms like Dremora, Golden Saints, Daedric Seducers, etc. are essentially like immortal humans, a full range of personalities available to them. However, while there is obviously more to the Daedra than we as players or mortals as mortals could know, if they are a mythic embodiment of something one would logically assume that they are near-constantly in a mindset related to it. Obviously, if a Daedroth is banished it gets a somewhat different personality when it returns (Dagon between Battlespire and Oblivion), but still simmilar enough to be recognizable as that primal idea. So I just put two and two together, and as far as that anology can go, I got the four of a Daedroth Prince being a fragmentary personality, one piece of the enourmous spectrum available and possible to Mortals.