What you are describing is something like an informal blockchain. Including prior messages ensures that new messages are presented in the context that their authors want them to be presented in. This approach resembles the back references that bind each block to its predecessors in a blockchain.
But you can't rely on this approach to ensure that surreptitious deletion of old messages or threads is impossible. Not every old message in a newsgroup will be duplicated within new messages, and threads will typically not reference each other.
If an old message or a separate thread provides necessary context for interpreting a new message, the maintainer of the newsgroup or the email server has the ability to change the meaning of a conversation simply by deleting messages or threads. Or the owner of a relay server can block certain messages from propagating. You still have to trust these people.
Email is itself very decentralized, at least in concept, with every new email being copied into multiple accounts on multiple servers, so censorship like this is more difficult. But you can imagine how in a more centralized system (like Facebook or Twitter or HN itself) history can be rewritten by the entity hosting the conversation simply by their deleting messages. If all references to the unwanted messages are also removed, then for all intents and purposes, those messages would never have existed. Gmail is dominant enough that you can imagine Google being able to assert this power over much of the email traffic that currently exists.
A blockchain ensures that every modification to the shared state follows rules that all participants in the system agree upon. No modification to that global state can occur unless those rules are strictly followed, and because all participants receive all details of every state modification, the entire history of the global state can be replayed at any time by any participant such that surreptitious deletion is not possible. There is no other technology that I am aware of that is able to systematically prevent surreptitious deletions.
Cryptocurrencies are not the only thing that is new, and they are not even the most important feature of blockchains. Cryptocurrencies function as an incentive mechanism to ensure that there are a healthy number participants validating the state transitions. They can improve the reliability and security of a blockchain system, but there are blockchain systems that do not depend upon them.