This technology called the Blockchain is built on the desire to create a new model to assure “trust”.
To establish trust between ourselves, we depend on individual third-parties.
Could there be a system where we can still transfer money without needing the bank?
This statement begs the question, What is a Bank. Is it simply an institution for recording the value we deposit with them and then allow us to move/transfer some portion of that value to another. This then means the loans a bank makes, based on the sum of the deposits we trust them with, is not part of what a bank does.
If the only role of the intermediary is to maintain a ledger capable of recording and facilitating the transfer to electronic facsimiles of something, then, yes a distributed ledger removes the need for the middle man the trusted intermediary. Instead of trusting a third party we agree to a methodology “The Distributed Ledger” to record these intangible assets or rights of ownership of a tangible asset in a manner where each of us has a copy of the ledger. The beauty of this concept is for someone to attempt to change a record in the ledger, recording the disposition of a tangible or intangible asset; 51% of us would have to agree to that alteration.
In the above-linked article, all of what happens can be summaries with this quote
Earlier the third-party/middleman gave us the trust that whatever they have written in the register will never be altered. In a distributed and decentralized system like ours, this seal will provide the trust instead.