Well, in this case it is still a permissionless blockchain. But there are many use cases why we need private permissioned blockchains. For example Hyperledger Fabric is mostly used for different purposes. You can find some use cases here: https://www.ibm.com/blockchain/business-use-cases.html
There's also Quorum, the open source enterprise blockchain based on Ethereum. It's got privacy and zksnarks and pluggable consensus and a decompiler and a consortium and everything.
