It seems like the tabs idea is geared more towards individuals that don't manage their email subscriptions (does no one unsubscribe anymore?). All I really know is that I am not the target audience for the feature.
Not all emails are created equally, and thus it is not a binary situation where emails either must all be treated equally, or they shouldn't be received.
I absolutely love the tabs -- my primary email gets better attention than it ever did, while the various promotions and LinkedIn updates, etc, all get the quick browsing periodically.
Honestly I probably pay more attention to the social/update/promotional emails than I ever did -- before I quickly tossed them aside while dealing with real stuff. Now during some downtime I switch on over to the promotional tab and see what deals are afoot, etc.