I for one understand the term, and I agree that, in the specialized and specific context of the debate about Nestorianism and the hypostatic union, the word "Theotokos" is correct in so far as the child that Mary bore was truly her own God. In that sense, and in no other sense, the word "Theotokos" is correct.

The use of such a term is unnecessary, as we can more easily say that Jesus is God and man and get across the actual point so much easier without confusion. The use of such a term is also misleading, as the normal use of "Mother of X" implies that the Mother created X, rather than that the Mother is just a means by which X comes into the world.

The term is also misused, as I frequently use Cathodox using it as a term of veneration or praise for Mary. When pressed, Cathodox will say that it's merely a statement about the nature of Jesus being truly God and doesn't imply any quality of Mary; if so, then there's no reason to use the term in Marian devotion as a laudatory address.

I'm a bit more comfortable with "God-bearer", as it lacks the implication of genesis that is present in "Mother".

The term was originally introduced as an easy way to clarify the discussion of Christ's two natures. It was supposed to make the discussion easier, to show exactly what the sides of the Nestorian controversy believed. Every time I've ever seen the term discussed, the people rejecting it had no interest in rejecting Chalcedon, other people insisted they absolutely had to be rejecting Chalcedon to reject the term, there were lengthy discussions about no, no that's not what it really means, and all kinds of confusion. It's clear that the term doesn't clarify anything anymore, and just leads to people arguing past each other and misunderstanding one another's arguments. It's no longer a quick clarifying term, and actually is less than useless at the moment.

Also...if you came into a physics conference and said that a term was stupid and should be changed, they'd probably just agree, and lament the fact that it's so widespread in the literature that now we'll never be able to correct it :P Most terms in physics are poorly picked. For instance, "quark". Quark is a kind of cottage cheese. Physicists don't usually insist that you have to use the specific term "Minkowski metric" or else you're denying the existence of spacetime.