I immediately had the same idea to use a 3rd part to host checksums, surprised they haven't done this. Blockchain makes a lot of sense from the immutability standpoint, but how would you incentivize people to maintain it? Maybe you can get people to do that for the common good a la wikipedia? Not sure about that. Maybe you get Apache to bake it into their webserver to ask people to opt-in to dedicate 0.1% of resources to the cause?
I was thinking about using an existing blockchain such as Bitcoin. Of course then the inconvenient is that archive.org would have to pay a fee every time they submit a new hash. A comment above pointed out that the scheme I described (unsurprisingly) already exists at https://petertodd.org/2016/opentimestamps-announcement
Realistically it might be overkill though, simply setting up some mailing list where anybody can subscribe and be sent the checksum every day or even just publishing it at some URL and letting users scrap it if they want might be sufficient. If we're talking about one checksum every day it's only a few kilobytes every year, it shouldn't be too difficult to convince a few hundred people and organizations around the world to mirror it.
Merkle trees.
Whomever wants to store a timestamp for some message stores the path from that message to the root of the Merkle tree. Only the root of the merkle tree of each day needs to be published.
