But you can't encrypt/decrypt with hash functions!

Oh yes I fucking can you anus-mouthed niggerian jew. I can trivially push this shit into counter mode and \(Ciphertext_{counter} = H(key \| nonce \| counter) \oplus Plaintext_{counter}\)

_{Use your favourite MAC construction instead of H!}

>>32

crypto can be used for both privacy and integrity

Encryption is used only to guarantee privacy. If you care about integrity you would use a WC-style universal MAC or a hash in a mac mode (sha3(key||msg), kmac, hmac, etc).