Why is a direct link to the case not always included in certain types of notifications?
This depends on how the notification is configured. A direct link to the case is automatically included if the message is sent to a registered user in the system—meaning the notification uses a person field to select the recipient.
If the notification is sent to an email address via the Email field type, no direct link is included. This is because recipients in these cases are not expected to have a user account in the system and therefore do not have access to the specific case.