Do you encrypt anything in that case? Or do things in such a way that no rogue employee of Inbox would be able to read someone's email?
I work with email currently, and one of the core mantras we have is that nobody should be able to read the email of someone who uses our service. It's such a personal thing with so much private information, that even the possibility of someone being able to do that (especially when there are more than a handful of us) is unpalatable to everyone here, to the point that we can't do common password recovery in order to keep that information private from us. I certainly hope you are/will take that into consideration as you build this.