The whole premise for changing the name seems faulty. The answer would better of have been to insure that correct teaching of the nature of who the Christ is would be instead of changing a title from one that is accurate and precise to one that is less so.
If the concern is heresy, I can’t see that changing the term to one less accurate would help that situation as opposed to the potential that it has to lead into MORE heresy.
You are right, Mother of God should not have been changed to Mother of Christ.
I may have not explained it well. Mother of God was the accepted title tell Nestorious began teaching his heresy, it was he who insisted on the title Mother of Christ.
Mother of God and Theotokos is very precise and is in complete agreement with orthodox Christology.
Pardon my simplicity here, but if Mary was the Mother of God, wouldn’t that mean that Mary had actually generated a member of the Trinity? And that He was a created being?