What parts of this problem aren't solved by archive.org?
There’s also the print archives, which are not available online.
It’s kind of what you signed up for when you started running a newspaper or news website.
No. I didn't actually. I probably signed up to produce (hopefully) quality journalism. But I didn't sign up to be an archive for the ages. And I'm not sure how I would even do so after I'm no longer there and have no revenues or employees. I can donate paper copies to the local library but that's basically just kicking the can down the road given that local libraries don't have infinite resources or space to maintain collections and, in fact, routinely sell off books that aren't checked out.
Now, is it the responsibility of organization X or person Y to preserve this value? I’m not sure, but that seems to be a separate (albeit also interesting) question.
One thought that comes to mind is that no site's reputation should automatically survive transfer of ownership of that site.
If a site's new owners share the mission and custodial mission of the original owners, fine. If not, the site starts from zilch. Or better: negative assertion value given the long history of link-farming and its exceedingly well-understood common weal costs.