I'd say there are a few ways to think about blockchain's utility in private contexts (public chains are pretty different because of their ability to allow for a

I'd say there are a few ways to think about blockchain's utility in private contexts (public chains are pretty different because of their ability to allow for anonymous participation). The two best ones are the intra- and inter-organization use cases. For intra-organization, one way to view private blockchains is to look back to the days of mainframes and the shift to databases. While you technically never need a DB and can get things done with code, DB's are incredibly useful as a general utility because of the baseline features you get by using one. Private blockchains are similar, in that they give you some new features (e.g. sharable DBs) and are much easier to build with as they raise the baseline on how bad a solution can be that is built with them. While you can have a pretty messed up DB schema, bespoke mainframe solutions can be much worse. Private blockchains are like that (especially when they have smart contracts) -- sure you can really mess up the systems setup but issues that DB's can have like high availability and disaster recovery are 100% commoditized. Also, they demand a higher bar for authorization making them generally as more robust the most hardened DB by default. That isn't to say that a private blockchain will replace the DB as blockchains can be wild overkill for many domains. A small company that needs a DB doesn't need a blockchain's feature set, but a large company that needs a globally distributed DB for holding a ledger (of anything) would be well served by one. When you're working with a system that by default is BFT, incredibly paranoid about authorization, perfectly replicated and highly available then build a solution gets much easier. As for the specific problem that they solve, it's the settlement problem: organizations currently hold internal ledgers of truth about what they own but they can't inherently trust other organizations' ledgers of truth about what they own, so we need 3rd parties to settle cross-ledger. Currently, institutions handle this role but private blockchains represent an algorithmic solution.