The thing is though you are talking about the game, not the world. All races can be Dragonborn, of course, in both game and lore. But the dialogue in the game can be very Nord-centric, and very warrior-centric, too.
The other thing I would mention also is the whole fighting dragons thing itself...that is very Nord-centric. The war between dragons and humans was essentially dragons vs. Nords. So in that respect, the game feels more 'right' when you play as a nord warrior, given the dialogue...depsite me playing as a Breton Spellsword

But certainly you are right about all races fitting, it's just that the point could have hit home more if the dialogue was expanded to match it.