Well... storage is cheap, but not cheap enough to save everything, with just usenet being in the 400TB/day range these days. Sure, it's cheap enough to save every webpage you visit during your life, but probably not cheap enough to save every video you click on youtube or watch on a streaming-service, and all the music you listen to all day.
Though just the music compressed in opus at 128kbit might work ok, 60 years of 24/7 128kbit is 30TB, so that would fit on 1 large HDD currently.
Music is actually an ideal candidate. I don't listen to music all day, and when I do listen to it, it's often something I've listened to before. My current collection is about 200GB and that includes a ton of stuff I've never listened to; it seems reasonable that a full life's worth of music could fit in 1TB, easily.
Though just the music compressed in opus at 128kbit might work ok, 60 years of 24/7 128kbit is 30TB, so that would fit on 1 large HDD currently.