The "blessing" mortals have over other beings is that they have a full range of personalities and ideas available to them, from lowest to highest, best to worst. While they all have just one (well, maybe a few in the case of multiple personality disorders, but that's a different can of worms) personality themselves, a mortal being could have had any one of them.
Contrast this with a Daedroth Prince. They do have "full" personality, of course, in fact one that is far deeper than any one full personality of a human. However, it is bound to a much more narrow range of options from rebirth to banishment. If you go with the dreamsleeve bit, a mortal will be spat back out with any personality possible, and the ability to have that changed and reformed without any sort of restriction outside of themselves (and even if, like me, you don't give much to the dreamsleeve, any new mortal born would have the same set of options). The Princes, by a set of mythic rules, will always have a set of parameters that they must adhere to as they return. Molag Bal must always be an embodiment of corruption. While there are always variations within each time he returns, there would be that unshakeable constant. Same with all the others, even the more "pleasant" Princes are stuck.
This leads me to the idea that they are somewhat jealous of Mortals, hence thier meddling in the mortal world. Azura is petty and easily prone to overreactive jealousy because she is already so. As a smart Prince, she may have discovered that her followers, even the reincarnated ones, have an infinite range of highs and lows, kindnesses and cruelties, while she has only one possible set with slight variations between any individual possibility. Dagon enjoys destroying things in the mortal realm more than others because he hates that he will never have the freedom inherent in the short, futile lives of mortal men. They meddle because they are jealous, and rankle at thier own lack of freedom.
So what do you think of my idea?