[wil5for]

This isn't quite the end state you're mentioning, but I've enjoyed using cloudKit ((https://developer.apple.com/icloud/cloudkit/)) as a developer and user in this space.

There's no setup on the user's part. For the developer, it allows you to abstract the datastore and give ownership back to the user - the developer doesn't have access to the private databases of its users. It's possible to build completely client side apps with syncing between devices without ever being exposed to the user's content.

Looks like CloudkitJs also exists for the web. I'm not sure if it allows the user to export directly, but that would help guarantee users weren't trapped.

All that said, it's tied to the Apple ecosystem. An independent service with similar features and a large enough community would be interesting.