I don't think she suffers from a lack of faith, but from an inability to feel the presence of God. To me, that seems egotistical. I know that a Creator exists, but I don't expect to feel the Creator's presence. That would be presumptuous of me. Instead, I see the Creator's hand in everything. That's good enough for me.
Mother Teresa's spiritual problems stem from her egotism. She wants to see herself as Christlike, as someone who has the capacity to suffer as much as Jesus did on the cross, maybe even to out-suffer him. She seemed to be appeased when her spiritual emptiness was pointed out to her as being comparable to Jesus' desolation when he was on the cross and cried out to God (asking 'My God, my God, why hast thou forsaken me?'). This strikes me as egotistical. She wants to feel closer to God by suffering as much as Jesus did, or more. I knew that her whole mindset was one of suffering, but I didn't understand the reason why, until the letters were revealed.
Actually, that makes some sense to me. I am not sure I would label it as egotistical. Perhaps the pride of self-righteousness? Whatever it can be labeled, I understand your point and see some validity to it.