The general scenario of hybrid encryption is to use public key cryptography for the exchange of a one time session key that can be used for the encryption of the plaintext with a symmetric encryption algorithm. A digital signature attached to that structure is what I know as a digital envelope. Furthermore, some resources agree that sign-encrypt-sign can help to prevent certain unlikely but possible attacks.
On the other hand, for strictly symmetric scenarios, the use of authenticated encryption is usually recommended as a default good practice.
Does it make sense to bring these two approaches together? Especially, would authenticated encryption (as opposed to semantically secure but unauthenticated encryption) provide any protection against any scenario not covered already by the digital signature?