I'm not sure this meets the definition of IDB but AA's offer is very generous to most of us.
As for the weather, airlines have minimum weather requirements at time of departure, en route, at potential diversion airports, and at projected arrival. Those requirements aren't obvious to the person on the ground. And while I certainly understand trying to get directly into SAF, considering it was a peak travel time, ABQ would look pretty attractive to me as an alternative under your circumstances. As for the DFW Hyatts, AA would certainly be happy to if they gave discounted rates to distressed travelers. The Hyatts don't do so, however, because they are able to charge premium rates because of their locations.