Is YouTube profitable yet?
I really doubt YouTube will last for centuries, or even twenty or thirty more years. There was a point where it seemed like Geocities was ubiquitous and would be around forever, and now it's gone. Internet services don't have a great track record for longevity. When YouTube finally goes kaput, much of its content will likely be lost, since I don't see Google going through the effort of offering archivists a dump.
Though, I'm kinda skeptical that even much digital data will last for centuries, unless formats and storage media ossify at some point on some long-term stable standard. The trend towards cloud storage makes things even more precarious.