Motability have a difficult job to do managing the scheme through the challenges of WLTP, EV introduction, a possible no deal Brexit with increased tariffs etc etc.
I believe that no private sector company would consider running a mobility scheme where the interests of the client were considered paramount, due to the constant scrutiny by government and media.
Motability have a sound financial base from which to manage the scheme through some unpredictable times ahead. A private company would not be either willing or able to commit huge reserves to guarantee that the scheme continues to provide such a dependable all inclusive service. (in my opinion of course)