I believe the Trinity is the most efficacious way for God to work through us and in us.
I reason like this: God is Our Father because He is the Creator of everything, the Father of all that exists. Why couldn't He be seen as a mother, then, the way some pagan peoples imagine the creator god? First, because a mother creates a baby out of her own substance. She and the baby are one until the baby is born. This is unlike the way that God created us. He created us out of a substance that is separate from Him: matter. As science has shown, this matter, or atoms, is the same material that all of God's Creation is made out of. God, however, is not made out of atoms. In other words, we, and the rest of Creation, are not made out of the same stuff as God.
Secondly, think about the Incarnation. If God were a mother, how would He have been a parent to Jesus? Would a mortal human have served as the Father? The thought is quite revolting! We know that Jesus's conception was planned from the beginning of time, so God knew that Jesus would have to have an earthly mother and a Heavenly Father in order to unite the human and divine natures.
At the same time, in order to avoid God having to "mate" with Mary, as the pagans believed happened with their gods and humans, a third agent is needed. This agent must be equal to God and part of the Godhead but able to act without the Other Two having to appear to us. This agent is the Holy Spirit. Imagine if God were one single entity, as Muslims believe. This would mean that in the Incarnation, Mary would in a sense have been impregnated by her own son! Clearly this is also unacceptable!
So we see that three Persons are needed to complete God's work. Why not four or five or ninety-six? I suppose because of God's own economy. So many persons are not needed and in fact might be confusing for us to comprehend. After all, the poor Muslims, and a few Protestants, are confused with just three!
That's my own weak manner of understanding it, anyway. I'm sure some of our other members can contribute something if they're not too busy arguing about how many antipopes there really are.