First, if it uses PRNG with a fixed-size state, it isn't accurate to say it never repeats, correct? It will be periodic eventually, even if that takes 2^256 operations or more.
Second, can you go more into the potential practical or theoretical advantages? Your scheme is certainly more complicated, but I don't see how it offers better tamper protection or secrecy than a block cipher operating in an authenticated mode (AES+GCM, for instance). Those have a number of practical advantages, like parallel encryption/decryption and ubiquitous hardware support.