Here's a fact sheet on the topic from the Air Force and another from the Federation of American Scientists website.

CRAF was activated for the first time in its history on 17 August 1990 when stage I aircraft were called up in response to Iraq's invasion of Kuwait. Despite a few minor problems, which have since been addressed, the activation of the CRAF was very successful. Commercial airlines are motivated to participate in the CRAF program in part by the opportunity to compete for DoD peacetime business. In the past several years, the volume of that available business base has been expanded by over a billion dollars. That was a strong factor in overcoming resistance to CRAF participation in the wake of the Gulf War. The possibility of opening up the DoD small package business to commercial carriers--another $200-$400 million--is now also being considered. Military airfields are being opened to CRAF carriers for operations and bad weather alternates as additional incentives for CRAF participation.

The key point is that the airlines do get something for participating. Given the terrible economic condition of so many airlines, activating the CRAF could be a blessing. Quite a few airlines have parked perfectly good planes in places like Mojave airport because they don't have enough business to keep them flying. They probably would go for those planes first before taking planes from profitable routes.