There would be other economic gains, too. South Korea currently imports nearly all of its energy and mineral needs. North Korea has vast deposits of coal, uranium, magnesite and rare-earth metals — together reportedly valued at $6 trillion — which it cannot currently exploit. Technology from the South could unlock these resources, boosting the economy of the entire peninsula.

Over time, a unified Korea could emerge as a regional consumer and industrial powerhouse — much like Germany, which today is the strongest economy in Europe despite having had to manage the costs and upheaval of merging West and East a quarter century ago. Goldman Sachs predicted in 2009 that if the Korean Peninsula were reunified, within 30 to 40 years it could overtake France, Germany and even Japan in terms of G.D.P., and become “the Germany of Asia.”

Considering all these benefits, the United States and its allies must revise their approach to North Korea. Rather than continue to prop up a government they worry might topple over on its own, they should pursue a tougher version of containment, knowing that that may accelerate the collapse of the Kim regime.

This harder policy would entail trying to cut off all the regime’s illicit sources of revenues, including drug smuggling, currency counterfeiting and exports of military equipment, while expanding sanctions to freeze all of Pyongyang’s overseas bank accounts. The House Foreign Affairs Committee approved legislation along these lines on May 29; that proposal deserves to become law. The United States government should also do more to undermine Pyongyang’s hold on its population by increasing broadcasting by Radio Free Asia and Voice of America.

All this may seem like a hard sell with the other states that are strategically invested in the region, especially China. But Washington could give assurances to Beijing that following unification, no American troops would be stationed north of the current demilitarized zone — or anywhere on the peninsula, if that’s what it takes to win China’s support. Nationalistic South Koreans, once relieved of the threat from the North, might insist on this anyway.

The fall of the Kim government may be an unnerving prospect, but it is a necessary step toward the reunification of the Korean Peninsula, a very worthy goal. Thus the United States, South Korea, Japan and China must abandon their soft-containment policy, which has artificially prolonged the regime’s existence. They should not be careful what they wish for.

Sue Mi Terry, a former C.I.A. analyst, is a senior research scholar at Columbia University’s Weatherhead East Asia Institute. This op-ed is adapted from an essay in the July/August 2014 issue of Foreign Affairs.