Unfortunately, the high cost of housing being what it is, young families HAVE to move out to Exurbia.
As far as Manhattan not gaining population, the main reason is that the only people who settle there these days are DINKs and SINKs, while the "ethnic" communities (blacks, Puerto Ricans, Dominicans, etc.) who typically do have children are leaving the island in droves (blacks to the South, Puerto Ricans to Orlando or New Jersey, Dominicans to New Jersey, the Bronx, or Westchester).