Moving beyond crypto currency and big banks,,,I have heard that block-chain processes(what ever those are) will be a new form of data storage and/or data security. That non crypto currency block chain will be useful.
The blockchain is created from currency transactions. The mining reward and transaction fees motivate the miners to keep 1000's of copies. The power of blockchain is that 1000's of miners agree 100% on the data in the blockchain. Withouth the miners there is no blockchain. Without cryptocurrency you will need some other way to motivate miners, otherwise it's just another Oracle database.
It’s already used for that. Especially handy for tracking items with complex possession chains, tracking that one chip from China to a circuit board in India, to a cellphone back in China to a Best Buy to you (through of course dozens of ships and trucks and shipping companies and manufacturing lines and sales people). The infinite insertion capability makes it really handy for that, doesn’t matter if your chain of possession for the item includes 3 stops or 300 you’ll never blow up the database or waste a bunch of space.