Trust is not binary.
Blockchains, via crypto, remove uncertainty from medium-trust relationships that would otherwise incur overhead due to counterparty risk, allowing one to replace it with the risk that e.g. SHA256 or ECDSA signatures have been broken, which is usually orders of magnitude lower than squishy human being behavior risks. (Presuming participating organizations have a way of keeping their keys safe, which is expensive but solved.)
That overhead is significant, and entire multibillion dollar industries exist around validating those trust relationships (accounting, auditing, settlement, et c).
Imagine if you could replace them with software that doesn't have to take anyone's word for it.
That's a big efficiency win.
They use blockchains because it is a fast way of conducting transactions relative to existing infrastructure that is architected based on incremental automation of manual processes. Transactions on a distributed ledger can clear quickly relative to standard send->ack->transmit->verify protocols with human scale execution times.
Is it all rosey and perfect? No. There are bugs in the system. There are bugs in every system including the existing system.
As far as I can see, blockchains only really make sense if they're protected by some sort of proof-of-work, in which case old data becomes increasingly difficult to alter as more blocks are added to the chain. To me, it appears that the concept of a blockchain was developed for this exact purpose in the first place, and that without this requirement (old blocks accumulating proof-of-work) there is no advantage to using a linked list of blocks.