The stuff that gets me excited is the more smart, automated, learning management. Alto is messing with some pretty cool stuff in that area. Just the simple act of automatically bunching emails without me intervening is a really compelling feature I think. It sort of takes away the concept of one big inbox. That automatic separate leads to all sorts of possibilites from just personal organization to analyzing certain "stacks" (to use an Alto term). I really don't know is best, but I can say that I've enjoyed that feature of Alto quite a lot.
Overall, I love seeing new takes on how to deal with email. There's certainly room for improvement and certainly some problems that can be solved. Keep the new ideas comin'!
I use labels a lot, but not only for importance/order of dealing with things – I use them to categorize/filter out of inbox as well. Which then, yes I do apply importance to (I have a few minutes, let me look through these promo emails or all these emails from basecamp).
So basically I use the labels to do "bulk importance labeling", but I wouldn't want to auto-tag all those "holiday sale" emails to "Later", and then just have to deal with them again later.
Your usage description ("Instead of fooling yourself into thinking you’ll tackle this today, simply mark it to reappear tomorrow or next week – when you’ll actually respond.") sounds like it's only talking about person-to-person needs-action types of emails. I think myself and many other people have a wider range of usage for email.
BUT that certainly doesn't mean Gmail's label approach is the only solution. But for people currently using labels a lot in Gmail, strong support for that paradigm is nice.
That doesn't work. Categorizations (labels)seems like a great way for me to use my inbox the same way as a GTD app. That's huge for me.
I get lost in my email and over-run pretty quickly, often missing things I need to do, or revisit. I think Mailbox is on to something here. People use their inbox as a todo list already, labels just makes it easier to pull off.
It's a pretty genius move.
The second is prioritization and "action markers." This is where labels aren't the optimal solution. Because the labels don't truly prioritize anything (your inbox doesn't get sorted by priority, except for "priority" and "everything else")--and it's a loosely ruled system--you need to define rules that result in actions to actually create priorities.
I think that's where Mailbox app will shine: it enforces a priority system. Whether or not it will eliminate the need for proper categorization for other purposes, though? I'm doubtful.