Seriously, though, imagine a public, distributed, append-only log, containing the hashes of the content stored by archive.is, with the data effectively signed by a (e.g. wallet) private key of the archive maintainers. People could volunteer to locally store copies of all the data that was archived, but only serve the data that goes "missing" from archive.is.
With such a dead man's switch in place, there would be no harm in archive.is taking down any content that they were threatened (legally or otherwise) over, and then other sites (hopefully too many to attack) could publish the taken down content, alongside the cryptographic proof that the data was originally published by archive.is.
You're right though that there would still be disruption, as the original archive.is links would (in the worst case) return unhelpful error pages.
I suppose I'm inspired by this idea:
https://www.reddit.com/r/Bitcoin/comments/6aiysw/the_whole_i...
You're also right that there is a huge cost to creating a secure blockchain from scratch, but the incremental cost of using an already secure public blockchain (such as Ethereum's) can be lower than the amount of value it brings to the table.
Proving the existence of data, at specific timestamps in the past, when keys may have later been compromised, does seem like a use case that requires tamper-proof distributed consensus between untrusted parties. Whether that use case is particularly valuable or not is harder to judge, though, I admit.