Her magic is.... odd.

Normally it's weak, taking a long time to do much of anything. She uses her staff to increase it's effect. She still can't do much more than mend a broken bone or fix a cracked bowl. She also tends to be exhausted after using it. 

As you said, nobody is around to train magic users, but L is a bit weird. Her magic is instinctual, it's a part of her, but she can't expand beyond what she does like most mages.