I always thought it was just general "now we control all magic, let's see you try to do anything against us using the thaumic equivalent of pointy sticks".
More than that, actually: The Age of Magic was supposedly a time of incredible acts of magical power because the magic was more concentrated. Now that there are people performing magic all over the place, we're stuck with lame effects like burning entire forests to the ground, causing deserts to bloom, making entire armies lose their will to fight, etc.
If the Tower of Mastery were to control all magic in the world, the controller of the tower would become nigh-omnipotent.
I always thought it was just general "now we control all magic, let's see you try to do anything against us using the thaumic equivalent of pointy sticks".
Well, maybe more appropriate to make it so all other Civs require Divine promotion in order to cast. You can't quite cut off the Gods themselves I'd say.