Anyway, there is no reason why you couldn't add a blockchain identifier to every block and it would not need to be part of the block hash. On the other hand, every blockchain is unique, so is it really necessary?
My idea is that adding a blockchain identifier to the block would allow miners to mine any of a myriad of Bitcoin-like coins on the same ASIC hardware and know which is which in the block. It would make the miners agnostic about the different blockchains of this type.