A blockchain is nothing more than a data structure. It is not even the thing that makes Bitcoin work. The thing that makes Bitcoin work is the decentralized consensus protocol.
A blockchain can be used to create an immutable ledger without decentralized protocols. Simple as that.
A private blockchain creates a cryptographically immutable record of data. How that data is appended and secured is where the differences come into play.
What is the use case? A decentralized, trustless system makes a lot of sense for a digital currency. For other use cases, not so much.
Blockchain will have many more applications than just cryptocurrencies. Many of those will be best suited towards decentralized, trustless control systems and many of them won't. The reward will come in recognizing the opportunities in the entire space and not by forcing particular structural elements into every possible application.