Short answer
The mission of the IMF does not include "democratic development". In its top ten members (by voting power) you have China and Russia. So it would be somewhat surprising to see those reforms in a near future.
Long answer
The truth is that a reform towards democracy is not the mission of IMF whose main objective is international financial stability and monetary cooperation:
The International Monetary Fund, or IMF, promotes international
financial stability and monetary cooperation. It also facilitates
international trade, promotes employment and sustainable economic
growth, and helps to reduce global poverty. The IMF is governed by and
accountable to its 189 member countries.
You should also be aware that IMF was created little after the Great Depression with the specific purpose of avoiding the decline of international trade, namely by making sure debts kept getting paid (wikipedia):
There were two views on the role the IMF should assume as a global
economic institution. American delegate Harry Dexter White foresaw an
IMF that functioned more like a bank, making sure that borrowing
states could repay their debts on time. Most of White's plan was
incorporated into the final acts adopted at Bretton Woods. British
economist John Maynard Keynes imagined that the IMF would be a
cooperative fund upon which member states could draw to maintain
economic activity and employment through periodic crises. This view
suggested an IMF that helped governments and to act as the United
States government had during the New Deal in response to World War II.
This is not part of your question but the reason for this is that unpaid debts tend to have a cascading effect with considerable collateral risks for other economies (I mean other than the indebted one). In this sense the mission of the IMF is relevant and within your own description of "establishing peace".
Nevertheless the IMF has been heavily criticized both in the past and today. Their structural adjustment programs tend to dictate the economical policy of the targeted nation usually by requiring privatizations, austerity measures, or cuts on subsidized sectors. This has often lead to the creation of private monopolies (where before there were public monopolies), rising inequality (short and medium term at least), and sometimes inability from the targeted nations of ever (or only temporarily) getting out of the programs. However notice that in general the success of the programs is considered adequate (in the sense of economic growth) for most cases (Schadler, 1996; Nelson & Wallace, 2016):
(Schadler, 1996)
In broad terms, the study concluded that the basic three-pronged
approach was appropriate. The approach did place a strong emphasis on
achieving balance of payments objectives, but this was inevitable in
light of limited access to external resources and the generally dire
balance of payments problems that brought countries to the IMF for
support
(Nelson and Wallace, 2016)
The findings presented here suggest that fears about the deleterious
impact of the IMF’s lending arrangements on democracy scores are
misplaced.
There was also a lot of criticism in the past about the influence of the US in IMF decisions. This has been somewhat reformed in 2015 but the quota system still remains problematic (the quota system is what gives the quantity of influence a member has over IMF decisions). Due to this and other reasons the IMF is still very much at the will of its stronger members (and in those top ten you have Russia and China). For these reasons I consider unlikely that in any foreseeable near future the IMF will start requiring "democratic development" as exchange for some boon.
