Vladimir Lossky sees this paradox and the implied apophatic attitude as part and parcel of Christian revelation:
"the transcendent God becomes immanent in the world, but in the very immanence of His economy, which leads to the incarnation and death on the cross, He reveals Himself as transcendent, as ontologically independent from all created being."
An apophatic approach then would hardly be optional. God is revealed as beyond our being, beyond being, beyond concept, time, space, thought and understanding. A positive approach (kataphatic theology) then, which affirms God is good, light, just, merciful etc., brings us to a certain point but ultimately falls short. Lossky posits that negative theology offers an "apprehension of supreme ignorance" and a mystical knowledge superior to the intellect, so here we start to see the usefulness of apophaticism:
"The negative way of the knowledge of God is an ascendant undertaking of the mind that progressively eliminates all positive attributes of the object it wishes to attain, in order to culminate finally in a kind of apprehension of supreme ignorance of Him who cannot be an object of knowledge."
So we can speak of knowledge, however it is a knowledge beyond our intellect. But would this not give way to gnosticism as a path to secret, deeper knowledge, or to provide subjectivism fertile ground? Not so if this mystical knowledge is not contrary to the rest of Christian revelation:
Just as iconographic "antinaturalistic" apophaticism is not iconoclasm, so also the antirationalistic negative way is not gnosimachian: it cannot result in the suppression of theological thought without detriment to the essential fact of Christianity: the incarnation of the Word, the central event of revelation, which makes iconography as well as theology possible.
Apophatic theology then is not the end of knowledge but a very necessary method to allows us to go beyond created being, indeed beyond ourselves. And that, to me, seems to be a good thing. Quotes are from Vladimir Lossky's "In the Image and Likeness of God". A related post with interesting comments in the combox can be found at Energetic Procession.