I don't understand why the member is unsubscribed rather than sending of emails being suspended like it would be for bouncing emails. That way they would still have online access.
That's an interesting idea. It resolves the objection to "No Email" by having a separate status instead of altering the member's delivery setting. Unlike bouncing though, this should be a group-specific status not something affecting delivery of messages from the member's other subscriptions.
It also begs a question of what, if any, indication the member is given on site. If there's nothing apart from that group being missing from the member's group list then I'd agree, a group-specific status would be friendlier.
On further question is whether this status should have a time-out after which it resolves to an unsubscription, or in the case of a subscription that actually wasn't desired does it end up hanging around forever. One of the reasons for the FBL mechanism is that some people use the Spam button to get rid of groups they've lost interest in because they're afraid to use an unsubscribe link.