Bringing 'Business Efficiency' to government was one of Bush's sellings points. Remember he was the 'Buisness President' and the 'CEO President'. They really hammered that before Enron fell, then their memories got hazy.
Cheney has been pushing towards more contracting in the military for decades. Rumsfeld is not fanatical about it, but it fits well with his own ideas of a new military organization built around high tech weapons, special forces and rapid response forces.
The invasion of Afganistan and Iraq proved that there where numerous problems with depending on contractors. Open bidding, contract oversight and negotiation of contracts break down when actually waging a war. One of the basic facts of a war is that everything needs to be done right now, it doesn't matter how it gets done, and cost is no object. Needless to say, companies are more then willing to exploit that for maximum profit at mininum effort on their part.
Jay