It depends, what would you consider lower magic.
I'll explain how i think of it. Lesser and "Higher/Greater" does not mean one is better than another. Lesser magics i generally think of as money magic, love magic, revenge, bindings, etc. Something geared towards influencing your physical circumstances.
Higher magics i generally think of as works of illumination, breaking of bads habits, reinforcinment of virtues, etc.
I think both types are neccessary. Remember these are loose definitions, and something can be equally greater or lesser. Though it really in the end does not matter. You may find lesser magic to be essentially higher, and higher to be lower.