Another apology. I should clarify that histories and files can be quite big, and transferring all of those via e-mail would be slow and put a heavy load on the relays. Profile and contact data would be comparatively compact.
Separate export of individual chat contents might complement a compact just-contacts-and-profiles transfer, especially if the chat-contents backup was encrypted using the keys in the profile backup. But if messages are ephemeral, then just abandoning the history would be a lot easier.