Websites don't really produce consistent content even from identical requests though.
But you also don't need to do this: all you need is a service which will attest that it saw a particular hashsum at a particular time. It's up to other mechanisms to prove what that means.
> Websites don't really produce consistent content even from identical requests though.
Often true in practice unfortunately, but to the extent that it is true, any approach that tries to use hashes to prove things to a third party is sunk. (We could imagine a timestamping service that allows some kind of post-download "normalisation" step to strip out content that varies between queries and then hash the results of that, but that doesn't seem practical to offer as a free service.)
> all you need is a service which will attest that it saw a particular hashsum at a particular time
Isn't that what I'm proposing?