Can LDS women be Sunday School Presidents?

From my understanding, women play a huge role in the LDS church, e.g. The Relief Society (which was established in 1842 and has about 6 million members). Even though they don't have the priesthood and as such don't serve as Bishops, Stake Presidents, etc., they still give talks and say prayers in Sacrament Meetings and are in charge of Primary, Young Women's, etc. But I don't understand why LDS women are not able to be Sunday School Presidents. They can be teachers, but not the presidents? What is the LDS doctrine behind that? Why must a Sunday School President be a priesthood holder if they are not overseeing priesthood ordinances? When anyone receives a calling in the LDS Church, they can receive inspiration for their stewards -- regardless of what their gender is, so I don't know why must a Sunday School President be a male, especially if priesthood activities are not involved. Is is mainly based on tradition? Or is their doctrine behind this?