Peer-to-peer solutions, including IPFS for file storage/serving and various solutions proposed here for decentralized messaging, are no good for battery-powered devices, like cell phones. I don't want mine to burn battery maintaining P2P connections 24/7, or burn battery and my time re-establishing or confirming cached connections every time I wake it up. That puts us back to having a gateway or proxy, so... a server.
Content on a p2p network would have built in guranteed of immutability. This would ensure that you wouldn't need to redownload the same content over and over, nor even check to see if you need to redownload it. If the GPs suggestion is followed, the resulting network could allow you to download content from a server just as you do now, so long as you pay the server to download from it. The advantage is that this server needn't be the original host.
On the other hand, a peer-to-peer solution would mean a better chance at connectivity when you're out in the field with your battery-powered device that's already consuming power to maintain what little connectivity it can get with the nearest cell tower.