The DS had established itself as a benign lifestyle device for people of all ages. Not only did it have cool games that emulated the days of the SNES for gamers, but it had a bunch of new stuff designed to attract non-gamers. Brain Age, Art Academy, Nintendogs, Picross, Crosswords and Personal Trainer: Cooking are just a few examples.
Thus, the DS XL seemed like a logical extension. The marketing made sense. Show grandma finally being able to enjoy her game with the XL (why should all the young whippersnappers with their good eyesight get to have all the fun?) or the family gathered around it in the kitchen making dinner (with the larger and louder speakers telling you when to take it out of the oven).