In a world of floating exchange rates and open capital markets, the IMF's raison d'être no longer exists. Its "clients" are rapidly repaying their outstanding loans. Macroeconomic accountability has improved world-wide, not because the fund mandates it but because without the guarantee of IMF rescues, investors now impose their own discipline. If hazards remain it is because, with the IMF still hanging around looking for work, future bailouts cannot be ruled out.
The IMF's sister, the World Bank, is also facing an existential crisis on its lending side. The bankers at the International Finance Corporation, which is dedicated to the private sector, now busy themselves financing big business, a job that ought to be left to the market. The bank's main business of lending to governments in middle-income countries -- that neither seek nor require bank loans -- is drying up. More broadly, foreign aid as a tool for development has increasingly come under scrutiny as wasteful and even counterproductive.
Usually, government bodies are more justifiable in the abstract than in reality. That is, the mission of a government body often seems to make sense, but then in practice the government agency cannot carry out its mission effectively without unintended consequences. For example, public schools arguably have a noble mission, but they are ineffective.
People can debate whether the IMF and the World Bank are effective. But, as the quote above indicates, their core missions also are in question. What role does the IMF play in macro stabilization when there are modern currency markets? (A Fischer Black view of the world would ask the same question about the Fed relative to domestic monetary policy.) What role does the World Bank play now that the New Institutional Economics (and some of the Bank's own research) says that the greatest barrier to development is not lack of capital but protectionism and corruption?