While magic and its limits are indeed defined by the author, the problem with fantasy worlds with widely available magic is that it usually ends up permeating the universe and being at the center of the story. Think of Harry Potter or LOTR or even going back in history to the tales of King Arthur. Game of Thrones is not a fantasy tale as much as a human one.

George Martin chose to make the story about people and the struggle for power and ideals and everything else that is human. And even with magic being barely a presence, it still is a force able to radically influence the game - but not much more than money, or armies, or human ability, which are still powerful enough to be relevant.

I think if magic was more widely available, it would either have needed to be trivial, not powerful magic, or these other resources would have suffered.