Would there be any benefit to symmetrically encrypting the IV and MAC in an AEAD mode of operation? More specifically would this prevent someone from exploiting the accidental use of a duplicate IV with the same key? Normally with most AEAD modes (and XOR-based stream ciphers) same IV + same key + different message = bad.
Example: let's say you have AES-GCM with a 64-bit IV and a 64-bit MAC / authentication tag. Now let's say after encrypting with AES-GCM you take the IV and MAC together and encrypt both with AES (using the same key or a derived key) in ECB mode (one 128-bit block) and send AES(IV|MAC) instead of sending the IV and MAC. Then at decrypt you AES decrypt that block and then run GCM with decryption and authentication check as usual.
If you duplicate an IV with a different message, the AES(IV|MAC) result will be different and since the IV and MAC are not visible in plaintext they can't be used by the attacker... right? (Obviously if both message and IV are identical the attacker can see that there was a duplicate of the same message, but that doesn't help them attack authentication for other messages.)
Other than costing a little bit of extra CPU does this help security? Am I missing something? This feels too simple to be novel.