Put another way, why does he require a violitional act of choosing God, rather than simply unilaterially saving humans from their fate?
One has to argue the premise - God doesn't necessarily need faith, he might just want it.
A truly compassionate and loving God who understands his people, may simply desire what is best for them. If God is the best, then it would be His desire that his people come to him- willingly and without coercion.
As an analogy, a father may understand that his children learn the value of money. That would entail getting the child's attention, showing correct courses of action, and rewarding desired / punishing undesired behavior. But, before any of this training can occur, the child must first believe that the parent knows how best to deal with money. Without that implicit faith, nothing can be taught.
Likewise, God demands faith (1) in order that he might help his children to be better.(2)
Yes, it does sound a little bit like an old Army ad, but its true: God wants you to be all you can be.
In order to accomplish that, however, one must choose (via free will) that God is in fact the best authority you can emulate.
God doesn't need our faith, he already has plenty of his own, it is we who need to develop faith. The question is why.
Every particle in the Universe ever acted upon by an intelligent being, is done through faith (at the very least we have to have faith that our perceptions are real). Every miracle ever performed was done through the power of faith – "by their faith they were healed.” Once in the celestial kingdom we will be able to create worlds of our own according to our faith.
Hebrews 11:5. “By Faith Enoch Was Translated that He Should Not See Death."
Remember that the idea of salvation is that God saves us from the penalty and power of our sins that He may have a loving relationship with us. Trust is an important foundation for any relationship to form and prosper. For instance, is any marriage relationship sound in which the spouses do not trust one another?
God has already gone out to us through the offering of His Son for our salvation. Faith on our part, trusting God, is our response to what He has done. (We believe in His finished work because believing in our works-righteousness will ultimately be fatal.) When we believe on the Son, when our hearts are hooked, then the "romance" begins.
Remember, too, that heretofore we have trusted in many other things, like in ourselves, society, mom and dad, money, good looks, and so on, to get us where we want to go. But God wants to take us in an entirely new direction, in which His kingdom values are to ultimately prevail within us. Trust will be key as we transition from one state to the next, groping along as we let go of cherished notions to grow in this foreign thing of trusting an invisible being. Faith in this God is important because we haven't been this way before.