I would call that portability (data portability, phone number portability, email portability, social graph portability, whatever), and reserve “self hosting” to mean at least operating (in some sense) your own infrastructure.
Owning and controlling your data are definitely huge with self-hosting. "Data sovereignty" is a good term for this.
Lately I've been thinking more and more how useful data locality and local first[1] / offline first are, too.