Every deputy see the mistakes their boss makes, knows they would never make such mistakes, would never become so out of touch with their own staff or so badly misjudge the mood of members, be so careless with partners trust or take for granted the loyalty of colleagues. Should the director leave or be forced out the deputy is ready to act up. Not to apply for the permanent post would be seen as lacking ambition or as signal that they were planning to go elsewhere so lacking loyalty to the organisation.
Of course they are never going to be offered the post because it is assumed there must be better candidates out there. Maybe if they can deliver the delayed restructuring, get the budget back on course, sacrifice management posts in the name of efficiency and offer up more cuts than were called as a demonstrate their corporate credentials they have a chance, they just need the time. Their motivation is simply a desire to serve during these uncertain times.