I agree this is a way to fundamentally root out mistrust. But what if this is not possible? What if the company just doesn't see the problem and therefore does not want to spend time on this extermination process?
I think every person can start by settting an example. Be counter-cultural! Show how the way you use email is more effective and productive. It's the long bottom-up approach, but this road empowers you, instead of waiting and complaining until "the rest of the company" gets it and starts the "improve trust program".