Inline with where we are taking the game, I was thinking we might want to strictly enforce spell components. And rather than eliminate types of magic (like mobility magic), maybe we change the spell components for certain magic so that it is impractical to cast it frequently?
For instance per the PHB levitate and fly don't take spell components (they take a focus which isn't consumed) but instead, maybe fly takes the long tail feather of a particular bird that is rare enough that we can control it. There might even be alternate versions of spells that take different components. For instance, a fly spell that uses feathers from some other bird.
I could review the spell components for the PHB spells and we could tell the players they can't use spells from other books without review by us. (Alternately, also along the lines of the training you've mentioned, maybe you have to be trained in all spells, even divine ones, and we can review the spells at the time we add them).