Precisely. Let the child retain citizenship, but eliminate the parent's ability to exploit that citizenship for his/her own benefit.
So are you going to deny that anchor baby citizen access to welfare programs like foodstamps and assistance to children programs that other minor citizens are eligble for? It seems then that you would be treating one citizen child very differently from another citizen child. If you deport the citizen child's illegal parents the child can either stay in America with legal relatives or go back to the parents country of origen. You are either denying the anchor citizen the opportunity for an American education or the opportunity to be raised by its parents.
I would prefer to not open these cans of worms by just giving the child the same citizenship as its parents.