The Jets want to have a GM running the personnel department and the head coaching running the team. Schottenheimer and Shanahan are two guys who clearly want to have final say over personnel decisions.
Also, the Jets want a coach who is going to be with them for a long-time. Marty and Mike might not fight that criteria.
And in all fairness to Schottenheimer and Shanahan, it's unclear if they even wanted the job.