This would give YouTube a unique feature that would keep their content producers hosting content on their platform.

However, the mechanics would be somewhat tricky. I'd guess it would work something like the following: submit a URL for a Facebook post/Wordpress post, that prompted YouTube to ContentID against your existing videos, and if it found a match, it put your flagged violation in a queue for human verification, and subsequent automated DMCA takedown gets sent to the hoster, along with a report of if the content is still available. Of course, that becomes open to the sort of abuse mentioned elsewhere in the thread.

FaceBook certainly have a team responding to DMCA requests. They are just slow.

Ideally, someone like YouTube licenses their technology, and opens up their contentID DB to the licensee for consumption... But again, I can see many avenues for abuse by licensee's (for example, automated "content capture" of content not currently in the DB), that would need good policies to help prevent.