In an answer of here someone mentions:
if you have a hash-function-with-oracle-powers, then it is rather easy to generate a pseudo random stream from a secret key, by hashing K||n where K is the secret key and n is a counter. By XORing this key-dependent pseudo-random stream with the data to encrypt, you have a stream cipher.
In the same post there is also this part regarding using cryptographic hash functions for creating a stream cipher:
A cryptographic hash function is a function which is resistant to preimages, second preimages, and collisions. As far as I know, it has not been proven that these conditions are sufficient to build a stream cipher.
As far as I know all of the currently existing symmetric algorithms, especially AES, are only believed to be secure. The only evidence we have in regards to their security is their use in practice and that attacks that have been tried so far were not catastrophically reducing the security of those algorithms.
Is the issue that "it has not been proven that these conditions are sufficient to build a stream cipher" really the only issue? What are other issues with stream ciphers that are induced by hash functions? Are they probably less secure? Are they probably slower? Are they probably using to much memory? Is it just that there are other encryption algorithms researched that promise better results?
I would assume a hash function with a larger block size has the advantage that longer keys or longer nonces could be used. For SHA-512 one could use a key with 384 bit and a nonce of 128 bit length. Another possibility would be to keep using 256 bit keys, use 128 bit nonces and have a better maximal message size of 2^128 blocks (or 2^137 bit for SHA-512) compared to ~2^39 bit for AES-GCM with only 96-bit nonces (which would be a nice goal in my opinion).