Prestige. The longer the wait to announce the death, the more important the dead person seems. I even had some arrogant TBM family members have two funerals--one in their ward in their home state, and another in Utah with all the Mormon relatives, at the mortuary where they were buried. This is really hard on the family.
Sometimes it might be because they want to notify family members before it hits the news. And, yes, Hinckley's death was pretty promptly announced, IIRC. I don't think that a reasonable delay is inappropriate if the family needs a little time to process things and to be sure that nobody hears about it first on the evening news.