There's already an app that I know of that does that - or at least close enough. Blendle is an app where you pay per article you read, paid through your in-app account. My uncle uses it to selectively read articles from some large publications.

I think one downside is that those publications don't let you sign in on their systems, so you have to rely on the availability of the articles through a third-party. I agree that it would be great to have publications allow you to sign in through a third party system instead of their own. Maybe we can hope for one in the future?