Iirc CalyxOS ships F-Droid by default and did include the F-Droid privileged extension, which enables unattended updates. This extension has to be installed in the system, which isn’t possible on stock ROMs.

They probably saw F-Droid Basic as a solution to no longer having to ship the privileged extension. I don’t think CalyxOS is shipping Aurora Store by default, but it also needed a privileged extension (until they supported the new unattended update mechanism two years ago).