If you're not using proof of work, blockchains start to look more like distributed storage with an audit trail and immutable row level db constraints

- if it's a Proof of Authority is like a way to deal with who has access to write to the db

- the distributed consensus part is well researched (Raft, Paxos etc)

The only advantage that I can think of is interoperability: you will be able to communicate with the public blockchain for point in time "backups". Also, building your internal smart contracts you can use an existing language like Solidity.