The web is already structured like this. You can poll a URL for updates. You can host your own data. Anyone can build an app that aggregates from everyone's data.
> Anyone can build an app that aggregates from everyone's data.
Unless they gut or disable their API, and then ban scrapers, although I understand why after seeing bots crush sites.
Yes, all of those things are possible. Now imagine a protocol built from the ground up for those purposes, not just possible, but the entire community and ecosystem embracing those things.