The ability to obtain any information at all about the underlying plaintext beyond what was pre-known to the attacker is still considered a success.
For example, if an adversary is sending ciphertext continuously to maintain traffic-flow security, it would be very useful to be able to distinguish real messages from nulls.
More advanced ciphertext-only attacks on the Enigma were mounted in Bletchley Park during World War II, by intelligently guessing plaintexts corresponding to intercepted ciphertexts.
The vetting process for a new cipher design standard usually takes many years and includes exhaustive testing of large quantities of ciphertext for any statistical departure from random noise.
Also, the field of steganography evolved, in part, to develop methods like mimic functions that allow one piece of data to adopt the statistical profile of another.