AES-CTR is nice for its parallelizability and simplicity but if you duplicate an IV you reveal plaintext.
Chaining modes like CFB and CBC don't have that problem per se but they are not parallelizable. (CBC-type modes have padding issues too but that's a separate problem.)
Naive ECB mode is not secure because it reveals structure in the plaintext as shown clearly here.
However if you added a counter to ECB mode and XORed each block of plaintext with the counter, you could avoid that problem.
The advantage over CTR as I see it is that duplicating a nonce/IV (or having no nonce/IV) would not allow actual plaintext recovery. It may reveal duplication, but that's it. In the no-IV case duplicate messages would have duplicate ciphertext, but that again only reveals message duplication but does not compromise secrecy.
Obviously you'd need some kind of padding but again that's a separate issue.
Why is this kind of mode not a thing? Would a mode like that have some problem I don't see or is it simply deemed unnecessary?