I've encountered some papers online describing ciphers made through a combination of stream and block ciphers. (See this 2008 paper by Sandy Harris: https://eprint.iacr.org/2008/473.pdf) In a nutshell, the concept is to use the output of a stream cipher to add whitening and/or update the round keys of a block cipher. The paper referenced above describes a combination of AES and RC4. Other examples of this concept I've seen are a cipher called Eris, combining HC128 and Serpent, and a cipher called Enchilada, combining ChaCha and Rijndael. Enchilada was an entry in the Caesar authenticated cipher contest but was withdrawn in the initial rounds.
The security claims for these combination ciphers are impressive. Standard attacks against the stream cipher portion should be thwarted by the block cipher, and attacks against the block cipher should be complicated by the use of unique round keys for each block of cipher text. The speed of these combination ciphers can be comparable to (or even better than) the block cipher by itself, because the number of rounds in the underlying ciphers can be reduced. (For example, Enchilada runs 12 rounds of ChaCha versus the standard 20, and Eris uses 24 round Serpent, versus the standard 32 rounds).
What I have not been able to find is any cryptanalysis or research on these types of combination ciphers. On the surface, and with my limited knowledge, there appear to be more advantages than disadvantages to this approach. At the very least, it looks like a promising topic for research. Yet the fact that there is so little information in the literature suggests these combination ciphers have flaws I am unaware of. Which brings me to my question: what are the disadvantages or weaknesses of this combined approach?