The ING paper continues "The fact that they [banks] do not (yet) provide custodian functions for Bitcoin (e.g. for regulatory reasons) does not mean that the general public would not need or want those services for cryptocurrency. In fact, many Bitcoin users choose to keep their wallets with online providers – meaning that even in today’s Bitcoin universe, there is a clear role for intermediaries."

The Bitcoin/blockchain-agnostic term for the basic abstraction these intermediaries share is "distributed ledger", though that doesn't solve the whole problem.

https://en.wikipedia.org/wiki/Distributed_ledger