Similar problems occur for PeerTube though - somebody needs to pay server costs, and for video that can be quite heavy. There's also no commercial concept behind it, so I doubt any instance of PeerTube feels a great need to get flooded with content. Where it really shines (at the moment) is when it is hosted by organizations (such as Blender or the European Union) to share their own content.
However, what's cool about PeerTube is hinted at in the name: it uses torrent technology, and whenever you're watching a video you are also seeding it to your peers (others who watch it). So while storage is an issue, bandwidth requirements are smaller than for centralized video services. So who knows what the future will bring. :)