If the Son is pre-existent with the Father (as Trinitarian theology asserts), then “Redeemer” is not part of his core identity. It is something the Son became on our behalf. “Redeemer” is a word that describes the Son’s relationship with us, not the essence of the Son’s being. Somehow that seems like an important point to me.

It makes God less inextricably intertwined with humanity. We are wholly dependent on God. God is in no way dependent on humanity. 
And it makes “Redeemer” even bigger because it was a voluntary choice on the part of the Son rather than something he just does because it’s in his nature. He is the Son. He chose to be Redeemer.