Here is a typical smart person’s thought about the IMF; the intro to the article reads:
When the IMF was a monitor of borrowers’ policies, dominance of the IMF
Board by creditor countries was natural, but an institution whose main
role is to facilitate global consultations and arbitrate currency
disputes needs a more balanced shareholder structure.
I again find myself drawn into a "public choice" response rather than an "optimization" response. I read the above sentence as stating the problem the IMF faces, not stating a solution. The U.S., Western Europe, and Japan support the IMF in large part because they control it. For the U.S. in particular the IMF has been a relatively good deal. You don’t have to think the IMF is especially effective (I don’t), but the institution allows for pre-arranged contributions to bailouts and pre-arranged coordination. Having a dominant hand in a multilateral institution works better for U.S. policymakers than having to assemble consortia on the spot, or explaining to some countries on a nation-to-nation basis that they won’t get any help.
If China and India had a significant voice in the IMF, what would they want? It’s not clear, and that is part of the problem. The U.S. isn’t about to stop paying its "country club dues," but when new upgraded members might someday form a blocking coalition, I’m not sure America will step up its contribution either.