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As far as I can remember, this is the first time we've gotten a request for that. If you email the support ninjas, they can add an item to the development database so we can consider that for inclusion in some future build of the app.

The general concept behind the current setup is that Project view is for planning, while context view is for actually doing things. Since the inbox is intended for stuff that you haven't fully thought out yet, we thought it would be a distraction.

Maybe a workaround would be to add a "Process my inbox" item that repeats on a daily basis? That would ensure that inbox items would get attention before too long.