Private blockchains are interesting, but only based on where they fit on that spectrum. Some people consider DPoS systems "permissioned blockchains" because only the elected block producers can produce. With PoW, anyone can spend money on a mining rig, turn it on, and produce blocks (in theory). Some private blockchains may make sense within, for example, a corporate structure or within a group of companies working together where data interoperability is a major cost and having a shared protocol use very useful for solving the coordination problem. It's similar, I guess, to a private database with decentralized nodes that has very clear specifications for how things work. Getting everyone to agree on that protocol can be tricky and having a governance mechanism to remove those who are not performing is also valuable, which a private blockchain could give, but it's still not unique to "blockchain technology" in a meaningful way, IMO.