Thats exactly what I do. I dont choose a character based on starting stat bonuses either. They're only good until maybe level 10 when everything starts to balance itself out. Thats whats great about this game. You play the kind of character and style you want to play, regardless of stereotype.

Exactly, the system isn't so rigid as to require sticking with stereotypes...sure it gives you a better footing early on but as you say, beyond level 10 it doesn't matter much.

I also have a Nord who's a pure mage and had a Bosmer who duel wielded waraxes and never touched a bow.

This is pretty much me. Bretons were my favorite race in Morrowind and they remain my favorite in Skyrim, and mages have always been my favorite class, so I've played a lot of Breton magic-using characters. However, I've also played Breton thieves and archers, and characters of other races and classes. I never liked playing the beast races, and I haven't played them in Skyrim, but I'm not totally ruling it out, either. If an idea pops into my head that would be an ideal roleplay and uses a Khajiit or Argonian (or an Orc, another race I've never played), I'm definitely going with it!