I've built a few API's using the complete rails stack. In each project there have been multiple uses for rails core features. Each of the API has had management screens for monitoring usage, managing authentication keys, etc. Is there such thing as an API without a management front end?
All your data, including Users and authentication could be stored and handled in an enterprise resource planning application and you Rails App is only an interface that provides certain views on the database that can be used by mobile Apps, employees, desktop Apps or whatever.