Malcolm Gladwell has an article in The New Yorker (13-20 Feb, 2006) that provides some interesting examples of where distribution (and by distribution I mean statistical distribution and not wealth) matters for public policy. Public policy towards problems such as homelessness, police brutality and car pollution is usually formulated as if the problem is concentrated around the mean of the group in question (as it would if things were normally distributed). However, in these cases it appears not to be. A few of the homeless have chronic conditions that soak up all of the expenses (in some cases millions per person). A few police are responsible for almost all incidents of brutality. And car pollution is caused by a smaller number of older cars.
What this means is that policies targetting the mean are not likely to be as effective as policies targetting the few. The problem is that the policies to target the few invariably help or single out the few -- something regarded as unfair. It is a very usefully argued point.
Sadly, Gladwell's argument suffers from an issue of history. We can't be sure that current and past policies directed at the mean are or did in fact assist in solving the problem at the mean and so created the power distribution that we see today. That said, if we are thinking of pouring more money in, then the distribution today matters.