As far as I understand, the whole point of a blockchain is to prevent failures of the kind where a node produces arbitrary data with malice - i.e., to guard against the case you don't trust some nodes of the network. If your nodes are trusted, though, a blockchain isn't necessary at all, you know the code isn't malicious. So what is the point of a permissioned blockchain?
If your nodes are trusted, though, a blockchain isn't necessary at all, you know the code isn't malicious. So what is the point of a permissioned blockchain?
Knowing someone's identity is not necessarily equivalent to trusting them, and not all trust is equivalent.
Consider the typical example of a permissioned blockchain. Two (or more) banks want to batch hundreds of payments a day into a single daily settlement payment. Each bank trusts the other banks to be solvent, and to pay whatever they owe. However, none of the banks trust the other banks to calculate the payments correctly. Instead, they all do the calculation separately, and only make payments if they agree about the result.
You could trust your business partners to do the calculation themselves, but they could give you the wrong number, either by accident, because of a rogue employee, or intentionally. Trusting someone's honesty is not the same thing as trusting their competence.
Let's also consider the opposite of the first example, where you don't know the identities of everyone involved. Imagine you have a Bitcoin sidechain, where instead of mining, a permissioned set of nodes creates blocks. In addition, instead of transaction fees, you give out API keys, which are permitted to create a certain number of transactions per hour. Some of the people who are creating transactions are people who you don't know.
In this example, you trust other nodes to not spam the network with useless transactions, but you don't allow them to spend other people's money, or create money out of thin air.