It’s obvious by the proliferation of systems to facilitate it (Snapchat, Cyberdust, etc.), that people are interested in having their communication protected by guaranteeing they are not permanent. There are two facets to it: 1. expire the message, and 2. do not have proof of who sent it. It’s good to have both even though one might be enough. The problem is with today’s systems: if you can see the message sent to you, you can record it by using another device like a camera and bypassing all of today’s “safety” mechanisms, and you end up having a record of what was sent and usually also by who.
This is only good for text but might solve the problems above. The sender types in the text. The app converts the text to a sound file of the spoken text. The audio file is sent to the recipient. The recipient can only listen to the message, and it expires after a certain amount of time (even if not listened to.) Although another device can record the spoken text, it is a mechanical sound, and there is no way to identify who sent it. You do see who sent it in the app, but you don’t see the message itself since its a sound. This way you have no way of recording both who sent it and what they sent in one “snapshot,” you only have two separate pieces of information with no way to prove they are connected.