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?
RSS/Atom feeds are exactly what you describe. And there are plenty of local-only RSS readers. I use newsboat personally. There are also GUI programs, and mobile apps, if that’s your preference.