IOTL, She's not really a grunge fan, and is more into Brit rock acts like Oasis and indie bands like Mercury Rev. Why pop? I dunno maybe to lay down the roots for a sound that can still evolve in to rock.
Good point, though I feel part of that is that she was so depressed her father killed himself when she was so young that she wanted to disassociate herself from the sound. Besides, I read in interviews that she would have been delighted if he didn't die and was able to raise her for a significantly longer period of time, so maybe his positive influence and encouragement doesn't turn her off from grunge and it's seen as a symbol of her adored father's image, rather then a tragic reminder of what potentially took his life. Maybe she plays a mixture?