Well, you could have only one user (such as the sender) hold the decryption key and be willing to securely send it only to the recipient within a given expiry..

Well, you could have only one user (such as the sender) hold the decryption key and be willing to securely send it only to the recipient within a given expiry... The distributed data could still be floating around but would be unreadable. There are plenty of distributed designs which could be secure and "read once within a time period". (btw, a distributed network topology can look isomorphic to a centralized topology at the application layer. You seem to have a highly simplistic map of the territory.)