If your peers are trusted you could do that. Or if you can agree on a central authority you could do that. But you are confusing trusted with known. I don't

If your peers are trusted you could do that. Or if you can agree on a central authority you could do that. But you are confusing trusted with known. I don't have to trust any given party in a private chain. I just have to trust the network. It's not difficult to come up with a private chain design that makes it very difficult for a malicious party to negatively impact. And you'd still have the immutability, known ordering and decentralisation amongst participants.