If you think of these govt agencies as employment-welfare themselves, makework jobs with a false veneer of productivity, it begins to make sense. The bureaucracy is the actual welfare program.
I always thought a much more plausible explanation was simply the accountability gap in public policy. The voters don't care if a policy works or not, they care if it sounds like it works according to their preconceived notions about how society functions (e.g. charging people to ride the bus will save money). Analyzing policy is a difficult and thankless task. It's hard to do right and voters don't pay attention anyway.
My suggestion: give each candidate 1/2 (or 1/3 or 1/4) of a ballot page to use as they please (with caveats on sourcing data). Let the infographic battles begin! It's not a perfect solution, but I think that it could do a great deal to steer the debate back in the correct direction: the post-mortem debunkings would likely be more socially productive than any immediate effect the graphics had on voter behavior.