p.s. Just to make clear, it is a good idea to download an archive, it just isn't used in the transfer process. The idea of the archive is to have a personal copy of everything you've posted.
The archive isn't currently readable by Mastodon, but it is readable by other software. Another Fediverse platform Calckey is currently testing a feature that lets you import posts from your old Mastodon account to your new Calckey account, and this uses your Mastodon archive.