A lot of welfare program spending never filters down to the poor. Social services bureaucraies take a large cut; the overhead percentage will vary greatly from place to place, but I imagine that on average it is very high. Then there is the gaming of the system, with large amounts being fraudulently siphoned off in improper payments to legally ineligble recipients. This leads to the always interesting question of how many $40,000 a year clerks, $80,000 a year investigators, and $120,000 a year supervisors you want to hire to chase people who are cheating SNAP for an extra $30 a month.
On top of that, you have to factor in the often massive incompetence and featherbedding of welfare services rendered in-kind rather than cash. I'm sure the situation varies greatly from place to place around the country, but here in DC, social services have notoriously been used as a jobs and political patronage program. I recall an expose of DC public housing years ago, back in Marion Barry days -- ancient history now -- that showed that it would have been significantly cheaper simply to shut the entire sytem dowm, and buy each public housing tenant a brand new townhome out in the suburbs. DC back then was probably an extreme case, and city administration has improved greatly since the Barry era (not that we're anywhere close to where we should be ...), but this is still a major factor. The system is short-stopping a lot of money that is intended for the poor.
A recent example from a different sector: DC as of 2010 was spending nearly $30,000 per year per student in DC Public Schools (DCPS), by far the highest figure in the country. That's almost Sidwell Friends tuition. While a handful of DC public schools have turned the corner and are noteworthy success stories, the DCPS system as a whole remains a disaster area, although one with a very large, very well paid staff and nearly as many non-teaching as teaching personnel. Welfare tends to work the same way.
If this thread is still alive tonight, I'll be glad to discuss solutions. Gotta get to work so I can pay my taxes. I have a whole lot of social workers and welfare administrators to support.
As to schools, I think we need to dump the entire concept of "mass education," as the goal itself is, in a sense, a contradiction in terms. The problems to be addressed in the aggregate of inner-city children are so integrated with the entire process of child-rearing in dysfunctional families, that to ask a bureaucracy to mitigate those impacts is exceedingly unlikely to succeed: The bureaucracy cannot be a family and the family to be served has no prospect of functionality.
In a sense, the focus upon "raising the bottom" destroys the wealth it takes to fund it. Hence, we should be building the willing by which to develop the capability of raising up the poor on an individual basis within the penumbra of a successful family: from servant, to intern, to protoge. In a sense, it is the conflation of this model (in the sense of functional responsibility) and this one (in terms of the educational tasks themselves), neither of which are the control freaks and their indentured consituencies of dependents going to be receptive.