FTR, when I refer to creativity, I am including a pass to the person who assists someone else. All that you mention (creative passing from the deep, defensive output, goals conceded) are measured by Opta one way or another. They're not perfect, but they're not going to give you a wild view on a player if you interpret them with some common sense. Carrick is simply average at all those facets (key passes, tackles, interceptions, etc). The one facet he is very high on is volume passing + accuracy. He was 3rd last year IIRC; Gerrard was 4th. In terms of chance creation, only Baines, Silva and Cazorla created more chances last year than Gerrard - Mata comes next.
Schweinsteiger and Xavi play almost the same exact role in their teams at both club level and national team. It's a similar role to Carrick, apart from the fact that they're much more mobile, get far more touches and are superior accurate passers.