I have a few thousand web pages on my site, blog posts, etc. Most of it won't be seen in any given day. So I have to pin it as it's realistically unlikely anyone else will. Not much different from today. This probably describes 90% of web content out there, where a single node is all that is keeping that content alive.
Now imagine something slightly more popular than my website. Maybe a particular Medium article. If it's two years old, it's unlikely to be getting any hits at this point, though it might have been popular at one time. So again, Medium has to pin it (or maybe the author would). Popular stuff would stay floating around while it's being viewed.
It's almost a dynamic CDN/torrent which could help with bandwidth, but I don't see any advantage for persistence in most cases.