PGP-signed messages, for example, are not only authenticated and of proven integrity, but they are nonrepudiable, at least cryptographically.
(Bad key management or other factors might affect any of these, but generally these are characteristics of the system.)
Designing a system which does allow for encryption and authentication but also provides for repudiability would be interesting.
The authentication output is only meaningful to the original conversation participants, because the only discernable difference between a real and a fake authentication even with access to all user keys and ciphertext is provenance - you know this output originated from a direct response to your cryptographic challenge, but nobody else can be sure you didn't just compose it yourself.
(Only the key-holders in a conversation between the "authenticatee" and challenger can generate valid looking answers for their specific pair of keys - either mutually between each other, or all by themselves in order to achieve repudiation)
However if a message payload itself consisted of, say, a PGP-signed message, then that could be authenticated independently (either on receipt, or if/when the public key was disclosed).
PRO:
- Enable changing of minds without being shackled to former identity?
CON:
- Now a statement that is incontestably true can be ILLEGAL and a LIABILITY if not immediately retracted
- Historical revisionism
- Memory hole