Why are blocks in a permissioned blockchain linked together?
I think you're mistaking PoW for a mechanism that guarantees the chain's correctness, rather than just a means for finding consensus.

A blockchain (without PoW) is just an ordered list of batched updates to a database.

PoW is one mechanism to guarantee that everyone eventually ends up on the same chain, but it doesn't guarantee that this chain is valid. Validity is enforced because non-miner full nodes actually validate all the operations in the chain to determine correctness.

If you remove PoW, you need another mechanism to obtain consensus. One way of doing that is having the block by signed by a trusted set of nodes. This means you're trusting those nodes to not sign multiple conflicting chains. However, it does not necessarily mean you trust them to assert validity of that chain. You can still have full nodes that verify that the chain being created is valid. In order to do that, your set of updates must be identifiable. A hash chain is one way of doing that.

If you're going to fully trust whatever your trusted parties sign without any validation, just use a replicated database instead. What a blockchain adds is simply a mechanism for identifying and auditing updates.

To be clear, I don't think there are all that many uses for permissioned blockchain technology, and a lot of the claimed advantages are hype. However, some of them will likely turn out to be a modern instantiation of BFT systems with auditability, and be boring but quite useful.