Yes, Tim-Berners Lee led the Solid project[1], which reverses the client/server identity and data model. The user will store their own data and the service provider can only access it under the policy set by the user.

The promise is that one can not only transfer the identity and all personal data across instances of a single service, but also across different services (imagine from mastodon to Lemmy).

Sadly, it never caught on.

[1]: https://solidproject.org/