It was Thatcher's government which discovered the benefits of creating "arms-length" agencies, starting with the Benefits Agency. It enabled ministers to distance themselves, to say, "Not me, gov," when anything went wrong. Privatisation compounds that lack of accountability. In the sphere of welfare-to-work Jim Knight, or whichever minister is in office, can be wheeled out to face questions, whether in Parliament or in the media, but can always claim that the figures are not available or waffle meaninglessly. Ofsted can produce poor inspection reports; parliamentary committees can take evidence from the companies' spokespeople and produce critical reports; but the companies are unaffected.
Obviously A4e is one of those companies which (unlike, for instance, Serco) thinks that publicity is a good thing - but on its own terms. "Benefit Busters" no doubt seemed like a good idea at the time. Emma Harrison can be turned into a media personality. A4e can use that, and its claim to be the largest welfare-to-work provider in the UK (is that still true?) to procure business abroad. But at the same time the system protects it from too much scrutiny of its practices, and protects the government from real accountability. No wonder the politicians don't want to change the system.