As far as I've seen, the point is mainly PR. These private blockchains are usually not bitcoin-style proof of work chains, but would more accurately just be called distributed databases. For example, look at https://www.openchain.org/, "How does it work" section. A lot of altcoins actually are the same, with explicit "trusted nodes", such as Stellar (https://www.stellarcoin.org).

Happy to learn about any counterexamples and use-cases for those.