The IA has tried distributing their stores, but nowhere near enough people actually put their storage where their mouths are.
In practice, that's mostly how they're being used.
But the protocol does support mutation. The BEP describing the behavior even has archive.org as an example...
> The intention is to allow publishers to serve content that might change over time in a more decentralized fashion. Consumers interested in the publisher's content only need to know their public key + optional salt. For instance, entities like Archive.org could publish their database dumps, and benefit from not having to maintain a central HTTP feed server to notify consumers about updates.