I've read somewhere that banks use blockchain internally. I mean levels of trust can be different within a company. Maybe you don't want anybody to be able to modify the ledger's history.
Of course, blockchain promoters would tell you that "there will be something else, comes Really Soon (tm) which won't use "proof of work"."
One can more efficiently use public key cryptography, hashing and signing without the blockchain for any other problem than "implementing bitcoin."