In a proof-of-work blockchain, the validity of the network is ensured by the hashes of each block pointing to the previous block. A "block on its own" would not be very trustworthy and, without all the CPU-work required to mine a block, it seems like there would be no reason to have a blockchain because the entire chain could be regenerated at zero cost.
So a network that didn't rely on proof-of-work at all would see little need for a blockchain, right? They could simply have a list of transactions organized by index, timestamp or some other type of organization. I don't see what value the blockchain (array with hash and pointer to previous block) provides over a traditional "ordered list of transactions" if there is no proof-of-work.