To me, a Dragonborn does not skulk in the shadows like a coward, nor does he use cheap magic tricks like illusion to take out his enemies. He slays them with a sword, axe, hammer, mace, whatever. I cannot see it any other way.
I think a destruction mage would make a great Dragonborn also, but because you cannot be a mighty destruction mage in Skyrim and have to resort to using cheap tricks, that simply does not fit the role.
Of course, many of you will have different opinions, I am look forward to hearing them. I am not saying I am correct in what I just said, only that it is how it seems to me personally.