Might be a rookie question. But exactly why would chat history not work?

I guess I owe a clarification: Otherwise your message history wouldn't be available the moment you log in with your credentials*.

This is a total misunderstanding of how E2EE works.

I need to either enter my password or let the app access my iCloud Keychain to let it derive the backup encryption key.

It's also well known that they worked with the Moxie's team to implement the same E2EE protocol as Signal. So messages are E2EE as well.