I'm in the early stages of bootstrapping a SaaS app that prioritizes security and privacy. For my business, this would be great: users are far more likely to trust an app if the app won't be storing any of the application data itself -- if they can choose their own data hosting provider.

Google Cloud Drive, Box, and others already allow this kind of model to an extent. Third-party apps can access and modify user data hosted there, although not through a standardized API.