What would happen to YouTube if one day there would be a message saying “We have been legally forced to verify that all the content we host are legal before we can make our service available again. A couple of hundred videos will be available by next week, and we will continue to verify that popular videos are legal and make them available. New videos could possibly be uploaded by the end of next year.”

YouTube would die.

And OneSwarm, etc, would explode in user activity (they have media preview, even for videos).

And remember that YouTube ain’t the #1 site I care about.
You know Twitter and it’s relationship with the Iranian people, and that delayed system update that would take hours? (They didn’t even want it to be down for a few hours if that delayed system update could help people)
You know every forum on the internet?
You know hard drive manufacturers?

Or is it free and open to be exploited to the extant allowable by the law under the guise of “free”?

At least they will defend this principle when the content is not claimed by a large corporate partner.
Those are pretty words.
Meaningless unless they are applied to everyone, equally