Well no, I don't want to hear a screaming baby anywhere, but I would certainly hope than most children over 4 or 5 could behave themselves long enough to allow their parents and the other diners to eat in peace, so banning them wouldn't be necessary.
I would rather not hear a screaming child or baby at any resturant I go. However at a five star restaurant I would expect that parents who bring their children to a classy restaurant would know if their children can behalf in an apporpiate manner. If not, I would hope they would go to the two or three star restaurants to teach them how to behave in public. I don't believe an age requirement is necessary.
No I don't think they should be banned. I don't think its fair. Remember you were once a child and I'm sure you at that age would have loved and be excited about going to a posh restaurant!