Well my understanding of the whole ramp-up to Ephesus and Chalcedon was the other way around -- a way I think you'd prefer: It was a Christological problem (as the article states) that raised the issue of Mary being the Theotokos. Stated too simply, if Jesus is the union in one person of the Divine and Human natures, then the child in the womb of Mary was God, and so it is proper to call Mary the God-Bearer -- the Mother of God.
As I was taught in my low-church Anglican seminary, Nestorius's objection to doing so arose out of his idea of how Jesus did not unite in His Person both natures, so the incarnation was not as "radical" or "complete" as we believe it to have been. Jesus REALLY is ONE person, He REALLY is God, He really is Human.
IF, on the other hand, Mary is NOT the Mother of God, then that which was born of her is not Divine. WHich is, well, a problem. So, to get back to your point, our Mariology arises out of and is consequent to our Christology.
And I'm confident - but have no evidence - that the Fathers were all too aware of how this might seem to be saying something like Juno or Leto or somebody was the mother of Apollo, but still felt that hey had to say that about Mary in order to hold onto the completeness of their doctrine about the Incarnation.
Again, I understand what the councils were trying to say.
Saying Mary is the mother of Jesus, however, does not say that Jesus was not God.