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.
Today's financial services firms might have massive computing power and fancy marketing speak, but from a customer's point of view they aren't very different from when men in stovepipe hats kept ledgers with fountain pens or when Captain Mainwaring sat in an oak-panelled office. To a typical bank customer, the only significant worthwhile innovation in the past 100 years has been the cashpoint machine. That's not much to show for decades of technical progress.
"Finance could and should be much cheaper" says Mr Philippon. So, how could it be made cheaper? One answer, he believes, is better regulation.
This, he says, should try harder to encourage new entrants. This matters because it is often new firms rather than incumbents that deliver new products; the car was not developed by makers of horse-drawn carriages. In practice, however, regulation favours incumbents at the expense of challengers. Big banks get a 'too big to fail' subsidy; the deadweight cost of complying with regulations bears harder upon new small firms than big existing ones; and the 'Frankenstein' complex (the tendency to be frightened by new technology) causes regulators to be warier of new innovations but tolerant of existing bad products.
However, I wonder if better regulation is sufficient. I fear instead that the barriers to innovation lie not just in bad regulation but in markets themselves.
One obstacle here is a classic market failure - that of externalities. Yale University's William Nordhaus has shown that innovators themselves capture only a "minuscule fraction" of the total returns to new products. The reasonable fear that the profits from innovation will be competed away might therefore inhibit the development of new products. This suggests there might be a role for the state or state agencies in developing new financial technologies. For example, the Bank of England's Victoria Cleland recently suggested that everyone in future might have access to a central bank-issued digital currency which would allow us to pay each other in real time without the need for commercial banks' clearing systems.
A second problem is that the Frankenstein complex isn't always wrong. Andrew Lo at MIT says financial innovation is a race between Moore's law (technology improves) and Murphy's law (if something can go wrong, it will). He points to the 'quant quake' of August 2007 in which many equity hedge funds suffered big losses. A big reason for this was that their algorithms put the funds into similar stocks, which meant that when one company tried to liquidate its positions quickly prices fell, imposing losses on other firms which where magnified by their own efforts to sell.
A similar fate could befall retail investors who rely on robo-advisers. Insofar as these recommend similar portfolios - which is possible insofar as (ignoring idiosyncratic risk) there is only one optimal portfolio - then losses for some funds could trigger fire sales which force prices down further, imposing big losses on everyone.
Or take another example. P2P lending might give lenders better returns. But these come at the price of exposing them more directly to cyclical risk. In a recession, defaults would increase, causing losses for even apparently diversified lenders. One of banks' few virtues is that they bear this risk themselves, thus protecting depositors from it.
But there's something else: demand for new products isn't as great as it might be. In recent years there's been an explosion in the number of cheap exchange traded funds, and we've known for years that tracker funds generally beat actively managed ones. And yet the actively managed industry still thrives. Why?
A big reason is customers' irrationality. Not only is there simple inertia - investors stick with the fund they have, just as we stick with our bank accounts - but there are also cognitive biases. The anchoring effect causes people to underestimate how horribly fund managers' fees compound over time. And overconfidence causes them to believe they have the ability to spot the minority of managers who can beat the market.
Irrationality, though, isn't the whole story. There's something else: trust. This is the basis of the financial services industry: we must trust whomever we hand our money to that they'll not mismanage it too egregiously. Big fund management groups such as Legal and General or Scottish Widows have spent decades cultivating an image of trustworthiness. Although the high-street banks have undermined this trust in recent years, this has not worked wholly to their disadvantage. Distrust extends to potential new entrants, limiting their ability to attract customers. Although challenger banks are doing well, they are still puny compared with the big four.
There are therefore powerful reasons why the paradox of the financial services industry will continue. Customers won't reap the full benefits of new technologies because a mix of bad regulation, market failure, distrust and cognitive biases will prevent competition from working fully.
However, perhaps we shouldn't single out the financial services industry. Utility companies, railways and broadband providers are also hardly paragons of efficiency and good value. Perhaps instead the point is that real-world markets often fall far short of the textbook ideals. As Adam Smith said: "There is a great deal of ruin in a nation."