When the entire nukes and missiles are under a central control, a launch would effectively state a fight to finish and be finished [MAD]. And I wonder ever if the BMD would act as a deterrent as with the case of US/Russia owing thousands of nukes and launch vehicles.

Even in the case of countries with smaller number of nukes ie India and Pakistan, a BMD development in India is now probably countered by an increased rate of nuke production by Pakistan.
I would like to know for whom would it cost more economically, in this case and to what extend the BMD is effective, assuming that fissile material is short?

One case the BMD is good to have would be if the non state elements succeed to make a launch, which has been identified and verified immediately by both government agencies, and need to be shot down without escalating the issue leading to MAD.