The Signal protocol already guarantees repudiation: https://en.wikipedia.org/wiki/Signal_Protocol#Properties
But this is just cryptographic repudiation, meaning that a receiver cannot prove that they didn't tamper with their Signal data to fake having received a message from a certain sender. OP is talking about something else: preventing any data the receiver might have received to be transferred to a 3rd-party, but that's impossible.
I think it is related to forward secrecy.
Maybe the E2EE apps should have a button for that, call it something snazzy like "The 5th Amendment button" and right next to that is a button for trivially forging texts and screenshots with the app's own UI, so that everyone knows that anything can be fake.