My question is closely related to Why do you need message authentication in addition to encryption?
Specifically I am interested in symmetric-key cryptography. I understand that attackers may modify cryptographic messages and the resulting decryption will be an altered message, MACs are designed to solve this. I read that one should create the cryptogram then generate a MAC from the cryptogram and send them together.
My question is why couldn't one simply append the original unencrypted message with a cryptographic hash of the original message and then encrypt them together? Then the receiver could decrypt both and verify the hash. If the cryptogram was altered the internal hash would no longer match and wouldn't it be hard to alter the message and/or internal hash such that they remain consistent since they are both encrypted?