I always say that a private blockchain is like a distributed database where every node is a master node (normally distributed databases only use one master node). Also in the distributed databases, there is no guarantee there is a way to know if your node has the most recent version of the database, in case of the blockchain you do.
Personally, I am in favour of the usage of private blockchain in order to improve the usability of the new generation of DApps. The current state of public blockchains such as Ethereum makes the implementation of DApps much harder due to its low performance (a tx might take several minutes to be confirmed) and the cost (around 0.02 USD per tx). Implementing a private blockchain you could have a finality of 2-3 seconds per tx and you could even make the tx cost-free for validator nodes (in case of PoS)
In think, groups of small companies will join together to build private blockchain sharing the cost of a distributed infrastructure and building new community economies which will eventually remove the control of big corporations such as Facebook, Gmail, etc.