I wouldn't say that library size is only tangentially relevant. After, all, if we all had small libraries, we wouldn't be worried about them as a valuable part of our estate, would we?
You're right, digital media bring all kinds of convenience and portability that make them valuable forms of media that should be transferable. (More important is that they should be transferable across formats/devices in time - I don't think my kids will be able to play my mp3s when I die :-)
But digital media uniquely encourage large library size - they are uniquely prone to accumulation.
How many times have you seen the following argument made, "If you made it easy to buy a digital copy legitimately, I wouldn't pirate?" Well, with successful stores (such as iTunes) the purchasing process has been made extremely easy.
What happens when you have extreme ease of purchase coupled with negligible storage cost? That's a recipe for inadvertent hoarding if I ever saw one!
Digital media enable us to lose all sense of scale of how much we have accumulated(because we have no physical objects to haul about. I don't think it's just a certain class of packrat that suffers, I think we all suffer from this loss of perspective.
It makes the question of transferability more acute to us, because we're investing more (money, time, attention) in gathering and consuming media than we would otherwise. So I stand by my original post - this is a first world problem :-)
Digital content enables a certain class of packrat, to be sure. But they're tangentially relevant, at best.