I would say first let us separate the issues here. One is the meaning of an annullment.
The other is whether certain influential people obtain them unworthily, or if too many are granted in general unworthily.
OK?
Now, I don't think anybody denies that the American Church has been way too loose in granting annullments. And I'm not about to tell you that a certain Kennedy is without influence.
So yes there are abuses. No doubt about it.
Now let's return to the definition of an annullment. It is a declaration that a valid marriage had never occurred.
However, this is not to make children of such a purported marriage "illegitimate."
The Church in general frowns on that type of labelling to begin with. No child is "illegitimate" in the eyes of God. A rapist's child in his victim is not deserving of death because of his father's crime and a child of a void marriage is not to be stigmatized.
If you want to talk about "legitimacy" of a child it is based not upon a later determinatino of fact, but the circumstances as they were known at the time. At the time of the children's birth, as far as anyone could determine, they were the product of a marriage. So they are as "legitimate" as any other children.
SD