Isn't that just a technical challenge? In this world view, you are your own central server and everyone else is their own. Let's take your example and run with it (bear in mind I'm ignoring some rough edges here). You share your instagram-style pics into an app on
your personal server to begin with and then from there they get federated out to people who've decided to 'follow' you (or those you have allowed to). Practically speaking, the pic (or rather
access to it) is given to the app on the personal servers of those followers.
Their server then constructs a newsfeed of all the incoming pics and presents it to their user (via an app or web-interface or whatever). This doesn't happen on the mobile device itself but on the 'personal cloud' of the user. There are many things I've glossed over but there doesn't have to be a central server in this scenario and everything can be encrypted end-to-end.
That's why this is really a distributed systems problem. In order for an app-developer to build such an app, the deeper problems around deployment, sync, and identity/connectivity need to be resolved. Developers just need something to target that provides the appropriate components. That's what the toolstack I previously linked is trying to solve. Without that, we're stuck with requiring someone else to provide the central system/aggregator. Clearly this is a non-trivial problem but if it can be cracked then it'll be as impactful as the opening up of the Web was.