Interestingly, the GDPR comes close to the requirement you suggest. It defines a "right to data portability"[0] saying that users "shall have the right to have [their] personal data transmitted directly from one controller to another, where technically feasible."

If this were interpreted by a court or regulator (perhaps as part of an EU anti-trust investigation) as a requirement to have new data automatically exported on an on-going basis, then that is very similar to requiring effectively federation between big services.

[0] https://gdpr-info.eu/art-20-gdpr/