But rationality is about how information is used, not just how much information is possessed. I don't quite understand how you can boil this down to the amount of information possessed? Especially when the manner of possession is so wildly different in each case (i.e. largely implicitly in the case of the market).Governments can therefore only make decisions on the incomplete information that they have. While the decision may be rational in that context in the larger societal context it may be completely irrational because of that missing information.
This is much like your comment on 'bad decisions' in which you left our the issue of the corresponding definition of 'good decisions'.The issue with market intervention is defining just what a market failure is. The term tends to be used very subjectively to define any market outcome which is contrary to the beliefs of the observer in question.
Is a minimum wage an appropriate intervention to prevent the market from failing to pay a 'fair wage'? Are debt-bubbles, capital flights, excess capacity, etc etc market failures or self-correction?
Certainly interventionists have the problem of defining what a market failure is, but similarly free-marketeers face the same problem with respect to optimality and non-failure (if they are to adequately defend their 'best of all possible worlds'-style analysis).
Also, I think that mainstream economics often makes the mistake of turning moral and political questions into technical debates. Take, for example, the debate you bring up regarding the minimum/fair wage. Technical facts are important, i.e. how will the market function in different institutional settings?, but we must also not forget that issues of fairness, standard of living and distribution of wealth also have a vital political dimension. I tend to feel that 'moral failings' in the market system warrant consideration, though in a different way, to mere technical failures.