Were it to work correctly I don't think it would be causing problems for the typical user and I'm not very sympathetic to the interests of marketers when considering how my inbox should be presented to me.
It's possibly a bit disturbing that on hacker news, this thread consists of three people all complaining that, effectively, 'This bayesian filter doesn't quite do exactly what I want out of the box, so it's clearly broken and/or I'm not the target audience for it', instead of acknowledging that bayesian filters aren't psychic, and considering putting in the few seconds per email it takes to train them when they make a mistake.
(Should those people have put dragged them to another tab - maybe 'Updates' rather than 'Promotions'? Possibly. If you think so, drag them to there instead. That'll change it for you, and presumably, if enough people do that it'll eventually change the categorisation for everyone who hasn't changed it themselves).
I could be misremembering, but IIRC when the new inbox first appeared it featured a popover over my inbox explaining how to drag and drop a miscategorized email into a different tab to train it.
I, too, have had very important ticketing and banking emails filtered into the "Promotions" tab. Good riddance! And thank you.
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.