I see. But there many scenarios where not reusing keys is impractical. And even if you never reuse keys, why not use a random nonce?
As a I said, encrypt-then-authentication is the only way mathematically proven to work with any secure encryption and authentication schemes. See the proof in, e.g., "Introduction to Modern Cryptography" by Katz & Lindell. If you use authenticate-then-encrypt, you may get an insecure scheme even if using secure cryptography & authentication schemes. (It may be secure for particular schemes, but it's much more safer to use the route that is guaranteed to work)