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?
There are many local ones but if you want to sync your subscriptions, categorizations and read markings, you need some server.
I use News Explorer which is Mac/iOS, runs locally, and uses iCloud to sync status++ between devices.