It sounds simple on the surface. You copy a link on a site into a feed reader app. Then whenever that site updates you get a nice readable article on the app.
But that sounds like something that could be accomplished locally. Why does every RSS reader I run into require an account or otherwise rely on the cloud?
NetNewsWire is a phone app that handles RSS locally - it just has to do a bunch of updating every time you open the app
You could also run FreshRSS locally and use a client
+1 for FreshRSS
+2