This depends on how you define “blockchain”. If your model is bitcoin-style with attempts at anonymous consensus it's definitely a negative contribution.
If you're not trying to get rich quick, however, something a Merkle tree is a great fit and it seems like there'd be value in a distributed system where trusted peers can vouch for either having seen the same content (even if they cannot distribute it due to copyright) or confirm that they saw you present a given object as having a certain hash at a specific time. Whether that's called a blockchain is a philosophical question but I think it'd be a good step up over self-publishing hashes since it'd avoid the need for people to know in advance what they'd like to archive.
To make that concrete, imagine if the web archiving space had some sort of distributed signature system like that. The first time the integrity of the Internet Archive is called into question, anyone on the internet who cared could check and see a provenance record something like this:
IA: URL x had SHA-512 y at time z
Library of Congress: URL x also had SHA-512 y at time [roughly z]
British Library: We didn't capture URL x around time z but we cross-signed the IA and LC manifests shortly after they crawled them and saw SHA-512 y
J. Random Volunteer Archivist: I also saw IA present that hash at that time
That'd give a high degree of confidence in many cases since these are automated systems and it'd lower the window where someone could modify data without getting caught, similar to how someone might be able to rewrite Git history without being noticed but only until someone else fetches the same repo.
(Disclaimer: I work at LC but not on web archiving and this comment is just my personal opinion on my own time)
That won't work because any hash on it's own would be trivial to regenerate after modifying the data. You need something that can't be changed retrospectively in order to trust it.
That's what makes the blockchain useful - to change anything you'd need to regenerate all the hashes after the point you want to modify. That's a lot more difficult. Having a proof that's generated by network of parties (like a cryptocurrency) would add to the trust level, but it's not essential.
EDIT: If the archive published hashes of everything they added daily in the NYT (or any publication) it would become unprintably large. It would only work digitally, at which point we're back to something that's trivial to modify...
Is it still possible to place classifieds in the NY Times? I don't think there's still anyway for someone to call up and have some random hash published, right?
I suspect the hardest part of doing that would be simply that you don't fit into their pre-existing categories.
FWIW, if you plan to do that, I'd suggest you put a Bitcoin block hash in the NY Times instead, which would prove the timestamps of everything that's been timestamped via Bitcoin. You can then timestamp your own stuff for free via OpenTimestamps, at which point your proof goes <your data> -> OpenTimestamps -> Bitcoin -> NY Times.
Timestamps are additive security, so it makes sense to publish them wisely. But if you're going to do that, might as well strengthen the security of as much stuff as possible in one go.