I keep wondering if there is any messaging application that a) does not store even encrypted contents or metadata after delivery (or timeout), b) encrypts the contents and the recipient's details between the sender and the server with a one-time key shared with the sender, c) introduces a random delay to thwart correlation analysis, d) pads the contents to prevent tracking by size (may be superfluous with encryption, but let's keep it in the list), e) re-encrypts the contents and the sender's details with a one-time key shared with the recipient, f) does not keep either the plain text or the encrypted content or the one-time keys or any logs after delivery, g) by default disallow (if possible) synching/backing up to "the cloud".
This will make it so much more difficult for the alphabet (isn't there a company called that?) soup agencies to do metadata analysis. Their remaining options will be restricted to intercepting at the server (or MITM to fake the key exchange), and that will hopefully be restricted to the provider's country of origin and will not give them access to the past history for at-will exploration.
Most of all, I wonder if there may be a business case for such a system (beyond being financed by the next OBL). Not obvious, given that it will be more complex, presumably more expensive to operate, possibly somewhat more cumbersome to use than WhatsApp.