Does God need/demand humans' faith for them to be saved? If so, why? According to soteriologies (e.g. Arminianism) that require humans to make a decision to come to God, why is that the case?  What does God gain from faith? 

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)


  (1) Heb 11:6 without faith it is impossible to please God, because anyone who comes to him must believe that he exists and that he rewards those who earnestly seek him
  
  (2) Heb 12:6 - 10 the Lord disciplines the one he loves, 
     and he chastens everyone he accepts as his son.” Endure hardship as discipline; God is treating you as his children. For what children are not disciplined by their father? If you are not disciplined—and everyone undergoes discipline—then you are not legitimate, not true sons and daughters at all. Moreover, we have all had human fathers who disciplined us and we respected them for it. How much more should we submit to the Father of spirits and live! They disciplined us for a little while as they thought best; but God disciplines us for our good, in order that we may share in his holiness


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.