Ok so one update on this issue. I've done some more testing. I am able to add other race's greater powers to a character, but I cannot remove the character's innate racial greater powers. I tested this on a Nord, Breton and Orc character. I could remove the "Active Effects" Resist Frost (Nord) and Resist Magic (Breton), but I cannot remove Battle Cry, Dragonskin or Berserk on any of them. Funny thing is, I can add those powers to the other ones and remove them at will. The game just won't let me touch their starting powers.
Is it just me? Is there any way to remove the starting power of a race? I just want to play a Nord character without Battle Cry/Resist Frost, and with Berserk instead.