I'm not convinced there's any internal use for blockchain. Internal implies under a specific umbrella, some overarching organisation, who can then be the central trusted server that makes blockchain unnecesary.
That said, non-public but open uses, such as tracking dealings between companies in markets with little trust and no single governments (the shipping example in your referenced comment) is indeed the thin slither of a plausible use-case.
Another limitation is that blockchain loses its benefits if anyone tries to design over the complexity of using it directly (using a ui that under the hood uses blockchain is no different to using a ui that talks to a central database, you're trusting the central ui provider, you need to (at least be able to) build your own interface to realise the benefits of blockchain.
That means blockchain basically will never benefit individuals, it can't. Sure, you could have multiple compatible uis shared around, but that's no different security-wise to multiple central banks with an interoperable transfer system.
The only place blockchain has real benefits is when multiple large corporations/governments are interacting and don't trust eachother/anyone.