One feature that I would like to have is a messaging tool inside the mobile phone app. Theses days the easiest way to send quick messages to the membership is through a messaging app. Right now we use WhatsApp but many folks refuse to use that because it is owned by Facebook.
Such a feature could be used for organization wide messages and members to member messages.
Yes, a direct channel to members would add significant utility to the mobile app, be it for general, individual or small group messaging.