With the difference that the Daedra don't give a **** about the Dragonborn - actually, on the contrary, they seem to be quite fond of the Dragonborn, judging by how easily they supply him/her with legendary artifacts. They do hate Aedra and some of the other Daedra, but mortals - why would they even care about them? They would be a pain to kill off and, besides, if mortals are gone then some of the princes, like Sanguine -especially Sanguine- would be bored to death... with the exception of one particular prince, daedric princes would not ever go to destroy anything in Nirn - they just make agreements or pranks to kill some time, they are not chaotic evil or anything, and some of them like Sheogorath are actually very pleasant folks to hang out with...
The Daedra Princes are always interested to acquire powerful mortals.
"So the Daedra Lords created the Daedric Realms, and all the ranks of Lesser Daedra, great and small. And, for the most part, the Daedra Lords were well pleased with this arrangement, for they always had worshippers and servants and playthings close to hand. But, at the same time, they sometimes looked with envy upon the Mortal Realms, for though mortals were foul and feeble and contemptible, their passions and ambitions were also far more surprising and entertaining than the antics of the Lesser Daedra. Thus do the Daedra Lords court and seduce certain amusing specimens of the Mortal Races, especially the passionate and powerful. It gives the Daedra Lords special pleasure to steal away from Shezarr and the Aedra the greatest and most ambitious mortals. 'Not only are you fools to mutilate yourselves,' gloat the Daedra Lords, 'But you cannot even keep the best pieces, which prefer the glory and power of the Daedra Lords to the feeble vulgarity of the mush-minded Aedra.'
http://www.imperial-library.info/content/monomyth