I think this is a misunderstanding. Those programs generally have low bureucratic overheads percentage-wise to begin with.
Some of the main benefits are 1) reducing welfare traps (accepting work doesn't cut your beneifits) and 2) encouraging independent behaviour by decreasing the stressful and dehumanizing busywork of continually reproving in various forms your entitlement to the benefits (and resulting economic uncertainty, mistakes derailing your finances)