Continuous Identity is not the same as public identity. Users decide what is visible to whom, down to the level of individual courses, credentials, affiliations, and activity. A doctor working on sensitive research can keep that work invisible while her general profile stays searchable — continuity and privacy are not a trade-off here, they are both defaults.
The default leans toward privacy. Everything published publicly is an affirmative choice. And the value runs in three directions at once: the individual learner building a lifelong, portable record; the expert whose reputation and body of work are the product and must be owned, not rented; and the organization that wants pre-verified members arriving in minutes rather than fresh-from-zero sign-ups it has to vet by hand. One identity layer. Three audiences who each win from it.