Blockchain is just bookkeeping. I don't know, can you demonstrate a use case for accounting or book keeping?
Up to now we always had to do accounting in books that can be cooked and have to be trusted.
Blockchain is accounting with books that can't be cooked and don't have to be trusted.
It has other problems which are real, but so what? Everything has some kind of problem.
With blockchain the problem is if you go for convenience and use a centralizing key custodian, then someone else controls your keys and everything they protect, and if you don't, then it's too easy to lose your keys and everything they protected with no recovery.
Well those are real problems but they are no different from the problems of using a plain database that can be copied, modified, hidden, stolen, has to be trusted even though you know you actually can't trust the owner, etc...
Blockchain has pretty powerful use cases in the enterprise. Ethereum provides one such solution which allows companies to have a private blockchain and programmable smart contracts in place—and with that a nice internal audit trail as well.
Blockchains can use proof-of-authority or proof-of-stake not as a means to accumulate “wealth” but firstly to secure the network from tampering while facilitating the resilient, chain of transaction records.
Ethereum is a distributed Turing machine (completely programmable)—first and foremost—and that is much more powerful than a simple coin.
Distributed programmable Turing machines are indeed very powerful. We're talking through a network of distributed programmable Turing machines right now. It does not involve a blockchain.
Academia is currently exploring multiple use cases, and some are already being used in real world scenarios. Permissioned blockchains for example can have multiple use cases in enterprise.
An example is supply chain management [0] and supply chain traceability, which is already in use at Walmart [1].
A few more that havent been mentioned: Source control, public cryptographic beacons (eg randomness beacons, beacons containing public keys). Chaining blocks with cryptography is actually very useful.
[1] https://merehead.com/blog/maersk-blockchain-use-case/
[2] Entirely possible this could be done without a blockchain, yes.