I think we call 'em smartphones. THose are the only things I know of that give a unified inbox view: at least for WP8 and BB10, they tie in contacts and conversations across mutliple social and email platforms and give you combined views.
However, you raise a good point - a nice cross-platform solution for desktop use would be a great thing to have. It's kind of odd that it's been done so well for phones, but barely touched for desktop.
One problem related will be the constant influx of 'services that may be interesting', with disparate APIs - any solution should have a good plugin system.
The Blackberry Hub (i.e., the unified inbox) is one of two reasons I'm still using a Blackberry (the other reason, of course, is the physical keyboard).
However, you raise a good point - a nice cross-platform solution for desktop use would be a great thing to have. It's kind of odd that it's been done so well for phones, but barely touched for desktop.
One problem related will be the constant influx of 'services that may be interesting', with disparate APIs - any solution should have a good plugin system.