In some churches there is a distinct place for intellectuals: they can be priests of certain sorts; they can teach in seminaries and schools for the ministry; they can take part in learned discussions among congregational leaders that will have an impact on the church or on individual congregations through them. There are no such venues of influence for Mormon intellectuals.
What, then, ought Mormon intellectuals to do? The first answer is "What everyone else does." Sit in the pews with your families and friends. When you find a speaker boring or inept, remember that others frequently find intellectuals boring and inept, and love the speaker through (rather than in spite of) the talk he gives. Clean the chapel, do your home teaching, set up chairs when needed.
Serve thoughtfully and faithfully where you are called to serve, not expecting special methods for intellectuals, special callings to suit our talents as we perceive them, or special classes to meet our "needs." Fast and pray often. Take part in the rites of the temple. Be thought of as Brother or Sister So-and-so rather than Mormon Intellectual So-and-so. In other words, we should do what everyone else does: stop thinking that we are special; be ordinary and learn to love ordinary life.
Learn to love the order of the ordinary and the divine influence that can manifest itself between the lines of that order, expecting neither that intellectuals will create the meaningfulness of the ordinary nor that they will significantly interrupt the course of the ordinary. God, not the intellectual, gives meaning to and disrupts the meaning of the ordinary. And he uses frail mortals to do so, sometimes intellectuals, more often not.
In the Book of Mormon Jacob tells us that it is good to be learned (2 Nephi 9:29). But if we do what everyone else does, what's the good of being an intellectual? Besides every other good, the good of being an intellectual is like all of the highest goods, it is to be good for nothing.
The place of the intellectual in the LDS Church is not to serve some purpose, to bring something about, or to change affairs any more than the place of any particular non-intellectual in the Church is to bring something about by means of their professions, personal passions, and interests. Whatever her other callings and good works in the Church, as an intellectual the intellectual is to be one who does not bring something about, who does not change affairs on purpose, who has no purpose, who simply is an intellectual beside, to the side of, what she does for the Church.
So: anything that is good in itself has no purpose beyond itself; strictly speaking, it is good for nothing else. That means as intellectuals (though not as ordinary members) Mormon intellectuals should, likewise, be good for nothing else.
To my mind, one of the best examples of Mormon intellectuals being good for nothing is Salt Press. (I am on the press's editorial board and have published an essay in one of its collections [An Experiment on the Word: Reading Alma 32].) Salt Press had its origins in the Mormon Theology Seminar, another theological project that has been good for nothing.
The Seminar has sponsored several seminar-style collaborations among five or six LDS scholars. Those collaborations have taken up particular Mormon texts of a few pages in length. They have done so in an on-line discussion requiring close reading and resulting in lively give and take over a period of three or four months.
The seminars have concluded with the participants writing a paper and presenting that paper in a small conference. All of the seminars are available as podcasts, and two of them have been published by Salt Press, the papers of the Alma 32 seminar and those of the 2 Nephi 26-27 seminar.
Salt Press also publishes books besides those resulting from the Seminars. All of its titles are published under a creative commons license, and sold at low-cost as print-on-demand publications or available free as PDF downloads.
The Mormon Theology Seminars and Salt Press do not exist in order to bring about anything at all. There is no agenda, hidden or otherwise, beyond thinking and talking together about Mormon texts, particularly scripture.
Were there to be such an agenda, then the intellectuals involved would have begun to suppose that they know something of themselves. They would have been unwilling to offer the gift of their work as a pure gift, expecting nothing in return, assuming that God and the Church will make of that work what they will—or won't. Instead what is needed from intellectuals is the pure gift of their intellect, with no demands or expectations attached.
It is difficult to remember because we are human, but the responsibility of the Mormon intellectual is, first, not to allow our intellects to separate us from the other members of the Church and, second, to work at being intellectually useless and, thereby, good for the Church on its own terms. We should be good for nothing except what the Kingdom demands.