No matter what the future of private blockchains might be, their best current use case is in the standardization of communication between various, likely disparate organisations. The whole "blockchain industry"'s best case for gaining traction is to pitch private blockchains as a part of a tech refresh cycle, and at the same time an opportunity to establish automated communication channels with their partners.
Blockchains do not make sense in isolation. it is a technology created to exchange information between multiple parties in a secure, authenticated and immutable way. A single company will have much better luck and significantly lower costs using a regular database for its internal needs than using a blockchain. Two or more companies which need to communicate with database-like data, could implement this communication in many ways, including building REST-like APIs manually, or they can make use of this combination of database-like functionality with strong data exchange emphasis and superlative data integrity guarantees we call a "blockchain."
But there's a catch - in order to communicate in any way, including by using blockchains, the organisations need to agree on the data formats and representations used for this communication. In most cases (Daisy being an exception), the blockchain software does not care what kind of data is being stored: XML, JSON and all sorts of binary blobs are perfectly acceptable all over the spectrum from Ethereum to Hyperledger, and it's up to the implementors to decide on, and implement the rules of, exactly how data is to be stored.
The modern, interconnected world, encourages and rewards tight communication in the market, even between nominal competitors. However, this communication has so far been implemented on as-needed basis, sometimes ad-hoc for specific projects, and it's not at all uncommon to find two large companies exchanging data in several different ways simultaneously, all built on different technologies-of-the-day at different times.
Blockchains can serve as a sort of an excuse for starting a new tech refresh cycle where all (or vast majority) of those communication channels built over several decades can be replaced by a single technology, with the added bonus of making the communication and stored data richer and more flexible (by using smart contracts), as well as reducing costs.
Of course, there's an implicit trap here: that by trying to replace N current technologies with a new, better one, we end up simply by having N+1 technologies in everyday use because the process failed or simply lasts for an eternity. There's also the usual problem of there being multiple competing products doing very similar things, which opens up the risk of several companies trying to connect with a blockchain - but alas each uses a different product.
In a nutshell, all of these conditions need to be true for a blockchain-ification of communication between organisations to be successful:
Multiple blockchain products are arriving to the phase where they are generally usable for the purpose of inter-organisational data exchange, so the next steps are to actually agree on the details.
