That's not MAC-then-encrypt, that's "ECB mode is pretty okay if your message and a nonce fits in your block" plus "let's make an arbitrary-length block cipher".

That's not MAC-then-encrypt, that's "ECB mode is pretty okay if your message and a nonce fits in your block" plus "let's make an arbitrary-length block cipher". In any case, the result is AEAD, not MAC-then-encrypt. (That said, AEZ is really interesting.)