1. Everyone makes a website.
2. Those websites submit articles to content indexes.
3. Part of your website hosts your own reader client:
3.a The reader subscribes to a set of indexes.
3.b It can also subscribe to individual feeds.
3.c Your client decides how to mix the feeds into displays, eg, you could have several indexes feed into one "feed" and have all of your family feeds in a second "feed".
4. Most of this is actually done via cloud hosting of managed packages, rented.
There's still many strong factors in favor of centralization, but if it's built around interop, then having a few large providers than mesh together is still an improvement and begins a competition to provide better services.
It's what happened with blogs and RSS anyway.