In Morrowind, I played the reincarnation of the Nerevar, the Chimer hero. Or not. But, whether or not you believe that you played the true Nerevarine, the main quest was still geared more towards Dunmer than any other race. Why would Nerevar reincarnate as a female Argonian? Why would Vvardenfell believe an Argonian (or, god forbid, an Imperial)? The fact was, you felt weird playing the main quest of Morrowind as anything other than a Dunmer (or at least an Altmer, for the closest physical resemblance to Nerevar).
In Oblivion, this aspect was slightly less prominent, but still there. The story sees you touring a number of Imperial sites supporting a distinctly Imperial cause. While it wouldn't be incredibly strange for a mer, Breton, or Nord to be the Champion of Cyrodiil, themain quest was obviously written with an Imperial player character in mind. Why would a Khajiit thief give two [censored] about the fate of the empire?
Now, we have Skyrim, where you are apparently the last in a long line of Nordic dragon slayers. Some of your line left to form the septim dynasty, while others died out. However...what would an Argonian be doing freezing his ass off in Skyrim with people thinking he's a Nordic dragon slayer?
I must admit, I would have preferred Fallout: New Vegas's style of starting you out as a complete nobody who isn't expected to fit a specific mold. Lately, TES has been making me feel as though I have to play a very specific type of character to fit into the verisimilitude of the world I'm playing in.