>What is the convincing advantage to centralize this in wikidata rather than letting the wikipedia communities handle this independently?

The objective is to create an extension that manages all structured data associated with any page, in a timely manner. There is already the SMW extension that does specifically this, but it has encountered puzzling technical resistance in the broad wiki administrator community I know from experience. From a social view, their resistance is explained by their sense of what their (normal) wiki users will tolerate, and it likely doesn't include managing structured data.

But more to the point is that NO extension need be installed for ANY wiki to directly benefit from the sheer existence of Wikidata - via simple transclusion of its resources. That cannot be said for the current proposal by which it indeed requires wiki administrator concurrence.