Media doesn't expire, but with increasing distance to the cultural context it was created in, enjoying any work in all its nuances becomes harder. Take for example Arrested Development - one of the funniest TV shows of this century, but unless you bring sufficient knowledge on the Bush Jr. administration, you'll miss the funniest layers of many jokes and stories.
And it gets all the more interesting to look back at how the Zeitgeist changed over time, as tropes evolve and tastes keep changing.
I don’t think people will ever really want to only watch old stuff, or lack desire for new stuff. But, in terms of thinking about the volume of media available I think the non-expiring idea is valid. YouTube alone has 500 hours of video uploaded every 1 minute.