This is the same inconsistent behaviour as I’ve found in which DAVdroid handles contacts and calendars. It’s quite confusing that for calendars, it’s enough to have share permissions to view/modify the calendar in order for it to show up in your available calendars, but for contacts you must “subscribe” for the shared address book to be available to the user.
Maybe it’s because there is are (proposed, but often used) standard for detecting shared calendars using calendar-proxy-read/write (which is used by DAVdroid), but there’s no such standard for address books. If this is the method how your shared calendars are detected, shared addressbooks can’t be detected the same way.
Technical details would be really helpful for deeper insights.