> public doesn't mean the {composer,artists,...} give up their copyrights.

Copyright law protects the original work of the composer and artists in your example.

User profile data on Linkedin is not Linkedin original work.

Additionally user profiles are mostly made up of facts, which are not copyrightable.

I think copyright as you mention here is the right concept, or at least a lot closer. In particular, the limits on copyright. If someone is reciting a list of facts in public, they can’t expect people not to record those facts, because copyright doesn’t apply to that. Reciting the list in public using computers shouldn’t change that.