All JWEs are encrypted using authenticated encryption with associated data (AEAD) algorithms. Is there any reason why you would not want to include the IV and Encrypted Content Encryption Key (CEK) in the Additional Authenticated Data (AAD)? Would it in some way make the JWE vulnerable?
Edit: I have continued researching this and found according to RFC 5116 Section 2.1
The nonce is authenticated internally to the algorithm, and it is not necessary to include it in the AD input. The nonce MAY be included in P or A if it is convenient to the application.
And
The secret key K MUST NOT be included in any of the other inputs (N, P, and A). (This restriction does not mean that the values of those inputs must be checked to ensure that they do not include substrings that match the key; instead, it means that the key must not be explicitly copied into those inputs.)
So my only remaining question is considering the encrypted content key is equivalent to a random value is it okay to also include that in the aad? Again entirely for convenience. Or would this cause a possible leak of information?