I would liken it to the development of technology in the real world. Has technology made the harvesting of food easier, faster, and more productive? By leaps and bounds, I'd say. Has the increased availability of said food ended world hunger or achieved world peace? Not even remotely. If anything, the increased level of technological development has just made the power struggles less overt at times, due to both sides possessing the capability for mass destruction (cold war, anyone?).
It seems that magic in this universe would follow a similar path of development. It may be everywhere, but that doesn't mean anyone can do anything with it. We all have brains, but it took the team working on the Manhattan Project to successfully develop an atom bomb. We've had access to the raw materials since the dawn of man, but had to first learn how to utilize them before they could be turned into what we know today as nuclear weapons. A thousand years ago, a box the size of a coffin that could destroy an entire city in a wave of fire and force would have been the most laughable flight of fancy. If it had been demonstrated, it would have been sorcery. In this realm, the roles are just reversed.
*drops two cents into the thread and toddles off*