A couple years ago, I devised some primitives for block ciphers and block cipher modes of operation; I was partly inspired by CAESAR. What these designs all had in common is that the encryption/decryption process would produce a bit string $T_i$ for each block and all of these bit strings would be combined together to make the authentication tag $T$.
Today I remembered some of the reasons why encrypt-then-MAC is preferred over other authentication methods, so now I'd like to know if the authenticated encryption schene described above is undesirable.