Take some examples. Crowdfunding could allow new companies to raise equity finance without incurring the high fees charged by investment banks; peer-to-peer lending platforms could connect savers and borrowers without bankers acting as middlemen and taking big cuts; cryptocurrencies might allow us to do without banks' payment systems; robo-advisers could replace expensive and sometimes inept human financial advisers; blockchains could allow financial data to be stored more cheaply. And so on.
History, however, tells us not to expect such great breakthroughs. This is because the last 100-plus years of technical progress have not much changed customers' experience of the financial industry. Thomas Philippon at Stern School of Business in New York estimates that the cost of financial intermediation in the US hasn't changed much since the late 19th century. And Guillaume Bazot at Paris School of Economics calculates that the cost of financial intermediation in the UK is higher now than it was in the 1950s. We see these costs in the gaps between banks' borrowing and lending rates, or in the hefty management fees charged by pension funds and unit trust providers.