I feel compelled to point out several things about Dremora here. As a lore nerd I find my jimmies rustled in a most unpleasant way. Forgive me for not citing sources, but if I have to I can track them down.
Dremorae are not hive-minded. They were not created by Mehrunes Dagon or for Mehrunes Dagon. Daedric Princes can create approximately dike. They were simply a group of similar spirits (Et'Ada) that formed in the beginning place. When Lorkhan proposed the creation of the mortal realm, they were among those who wanted nothing to do with it, and they rallied around the various princes that existed. Due to the nebulous nature of Mehrunes Dagon's origin -- he seems to have been an Aedroth that aided Lorkhan in foiling Alduin's world-devouring, according to Seven Fights of the Aldudagga -- it's hard to say precisely when the Dremorae decided to serve him, but it's definitely for a long time.
Now their clan ties are the main reason we'd never see a Dremora PC, unless this was a game taking place in the planes of Oblivion. Honor is everything to the Dremorae. An individual Dremora turning his back on his clan and kin would suffer great dishonor, and that's just plain unthinkable. Loyalty, power, and honor are the core of a Dremora's existence. They can't turn on that. It's simply their nature.
As for why they can't be Dragonborn: well, they said that a Dragonborn is a mortal born with a dragon's soul. This is impossible for a Dremora because a Dremora is a soul.
Thank you for explaining everything I was too lazy to. No sources needed.
Everything said in this post is right, for whatever my word is worth.