So I can't provide a strictly bank-oriented response, but blockchain is just a distributed ledger system. I think some disservice is done in not clearly separating out the functions of blockchain from those of cryptocurrencies. You could use blockchain to manage property, contracts, microtransactions, data commerce, file storage, or certification, to name a few things. I think it's mostly a question of what can be fit into the ledger framework. Some people think that various local networks and other functionalities in the Internet of Things could be a testing ground for its broader uses (e.g., managing ownership of smart devices). Blockstack envisions it as kind of a backbone for a new Internet browsing paradigm, leveraging blockchain as a sort of DNS replacement if memory serves correctly. It's unclear if any of these ideas will take off in the near term.
Going back to these blockchain applications being separate from cryptocurrencies, to me Ethereum is a step away from the coupling of the two, because it is designed with contracts in mind rather than just money. And a number of folks have signed on to developing systems that leverage Ethereum - take a look at the Enterprise Ethereum Alliance. Still I suspect that given the fact that it's unproven, the actual investment made in personnel and capital by these firms is low. Also, the ironic counterpoint to this view is that Ethereum also has ETH, a cryptocurrency. I'm an investor in ETH, but even so, I am not sure what it is worth at this point, since the value of Ethereum seems to lie not in currency but in other applications of the blockchain.
Except the examples you give demonstrate two widely divergent use cases - public and private. If you are managing an internal database, you don't need proof of work. You need concurrent conflict resolution. Every major database right now has such faculties built in and you don't need to spend megawatts of power to maintain it.
In the public dns replacement use case there is promise and potential, but it has the laundry list of problems you would need to solve to make it happen. I look forward to the attempts, of course, because traditional dns is a brittle top down nightmare of exploitable corruption and manipulation.
But still, blockchains as they are are only useful when you don't trust participants. And for along large-scale application, making that claim puts you in a political position - either you trust or distrust the governments oversight of whatever you are trying to reach consensus on. While a lot of people will, at inquiry, say they don't trust the government, very few people are willing to put the effort into forging an alternative public trust framework for things like property rights or certification that you mentioned.
I agree with you that the public use case makes more sense than the private one, though really I feel that it's not about "public" or "private" but rather about different sides in some market, whether it is public or private.
But I'm not sure I understand, were any of those use cases "private?" When I mentioned "manage property, contracts, microtransactions, data commerce, file storage, or certification, to name a few things", I think pretty much all of those besides file storage (on which I'd defer to Blockstack) represent agreements or exchanges between different sides in a market or platform.
Going back to these blockchain applications being separate from cryptocurrencies, to me Ethereum is a step away from the coupling of the two, because it is designed with contracts in mind rather than just money. And a number of folks have signed on to developing systems that leverage Ethereum - take a look at the Enterprise Ethereum Alliance. Still I suspect that given the fact that it's unproven, the actual investment made in personnel and capital by these firms is low. Also, the ironic counterpoint to this view is that Ethereum also has ETH, a cryptocurrency. I'm an investor in ETH, but even so, I am not sure what it is worth at this point, since the value of Ethereum seems to lie not in currency but in other applications of the blockchain.