On the other hand, * I * think that it is a way to prevent having to incinerate babies by the millions. ( Which is the entire basis of MAD)

It can't prevent the scenario I described, and for this reason, we know it can't prevent the incineration of babies by the millions. It can only prevent it from being accomplished by a missile strike. This is why it is not defensive in nature, but rather, is for the purpose of creating a first strike capability. This system cannot prevent someone with the desire to nuke this country from doing so if they are determined. The only thing this system can to is ensure that if the US nukes another country first, that other country won't be able to nuke us or the part of Europe covered by our system in retaliation, using a missile.