The world is awash in paper currency, with major central banks pumping out hundreds of billions of dollars’ worth each year, mainly in very large denomination notes such as the $100 bill. The $100 bill accounts for almost 80% of the US’s stunning $4,200 (£3,152) per capita cash supply. The ¥10,000 note (£72) accounts for roughly 90% of all Japan’s currency, where per capita cash holdings are almost $7,000. And, as I have been arguing for two decades, all this cash is facilitating growth mainly in the underground economy, not the legal one.

I am not advocating a cashless society, which will be neither feasible nor desirable anytime soon. But a less-cash society would be a fairer and safer place.

With the growth of debit cards, electronic transfers, and mobile payments, the use of cash has long been declining in the legal economy, especially for medium and large-size transactions. Central bank surveys show that only a small percentage of large-denomination notes are being held and used by ordinary people or businesses.

Cash facilitates crime because it is anonymous, and big bills are especially problematic because they are so easy to carry and conceal. A million dollars in $100 notes fits into a briefcase, a million euros in €500 notes fits into a purse.

Sure, there are plenty of ways to bribe officials, engage in financial crime, and evade taxes without paper currency. But most involve very high transaction costs (for example, uncut diamonds), or risk of detection (say, bank transfers or credit card payments).

Yes, new-age crypto-currencies such as bitcoin, if not completely invulnerable to detection, are almost so. But their value sharply fluctuates, and governments have many tools with which they can restrict their use – for example, by preventing them from being tendered at banks or retail stores. Cash is unique in its liquidity and near-universal acceptance.

The costs of tax evasion alone are staggering, perhaps $700bn a year in the United States (including federal, state, and local taxes), and even more in high-tax Europe. Crime and corruption, though difficult to quantify, almost surely generate even greater costs. Think not just of illegal drugs and racketeering, but also of human trafficking, terrorism, and extortion.

Moreover, cash payments by employers to undocumented workers are a principal driver of illegal immigration. Scaling back the use of cash is a far more humane way to limit immigration than building barbed-wire fences.

If governments were not so drunk from the profits they make by printing paper currency, they might wake up to the costs. There has been a little movement of late. The European Central Bank recently announced it will phase out its €500 mega-note. Still, this long overdue change was implemented against enormous resistance from cash-loving Germany and Austria. Yet even in northern Europe, reported per capita holdings of currency are still quite modest relative to the massive outstanding supply in the eurozone as a whole (over €3,000 per capita).

Southern European governments, desperate to raise tax revenue, have been taking matters into their own hands, even though they do not control note issuance. For example, Greece and Italy have been trying to discourage cash use by capping retail cash purchases (at €1,500 and €1,000, respectively).

Obviously, cash remains important for small everyday transactions, and for protecting privacy. Northern European central bankers who favour the status quo like to quote Russian novelist Fyodor Dostoyevsky: “Money is coined liberty.” Of course, Dostoyevsky was referring to life in a mid-19th century Tsarist prison, not a modern liberal state. Still, the northern Europeans have a point. The question is whether the current system has the balance right. I would argue that it clearly does not.

A plan for reining-in paper currency should be guided by three principles. First, it is important to allow ordinary citizens to continue using cash for convenience and to make reasonable-size anonymous purchases, while undermining the business models of those engaged in large, repeated anonymous transactions on a wholesale level. Second, any plan should move very gradually (think a decade or two), to allow adaptations and mid-course corrections as unexpected problems arise. And, third, reforms must be sensitive to the needs of low-income households, especially those that are unbanked.

In my new book, The Curse of Cash, I offer a plan that involves very gradually phasing out large notes, while leaving small notes ($10 and below) in circulation indefinitely. The plan provides for financial inclusion by offering low-income households free debit accounts, which could also be used to make government transfer payments. This last step is one that some countries, such as Denmark and Sweden, have already taken.

Scaling back paper currency would hardly end crime and tax evasion; but it would force the underground economy to employ riskier and less liquid payment devices. Cash may seem like a small, unimportant thing in today’s hi-tech financial world, but the benefits of phasing out most paper currency are a lot larger than you might think.