I've been informed by a reliable source that the only reason that there is any Grand Prix coverage on NBC at all is because U.S. Figure Skating bought the limited rights from Universal Sports (apparently NBC does not own the broadcast rights to any ISU events besides Skate America?) and sold the advertising in order to make the telecasts possible.
My guess is that short programs are rarely shown these days because NBC has elected to do the least amount of video editing and post-production work possible in order to keep down their costs in putting together the telecasts.
However, I don't see why we fans shouldn't still request that NBC make improvements in their coverage, such as showing the top pairs' and dance teams' performances (in addition to Davis/White and Virtue/Moir), the best short programs, etc. in a 2013 Worlds recap telecast IF one is scheduled to happen.