The importance of that kind of leaders lies in their skill to drastically turn companies from a downfall into a success that is maintained after their reign is over. They are more concerned for the goodwill of the company than their own personal fame and fortune. In fact, they dread recognition and tend to grant credits to the organization and the actual employees.
Following a 5-year research, based on the fortune 500 companies, only 11 experienced the exceptional turnaround mentioned above and were able to maintain it. All of which had level 5 leaders on top at the time when the transformation took shape. Quite a remarkable finding.
Could that type of introverted leadership be qualified by a superior EQ level? Think of it this way. If a CEO takes credit for the work of the organization, how would it effect the rest of the staff's motivation? When one person is granted the fruits of their labors, employees feel used. If the level 5 leaders do not take credit for the firm's success, it is probably not because they don't think they deserve it; rather that they understand how people function and know how to behave to gain the respect of their co-workers. This is emotional intelligence by excellence. Do those people lack the critical skill of EQ, as defined by Daniel Goleman, that is "awareness" of their capabilities? I think not. Their modesty is part of their job. This can be attributed to another characteristic that qualify their Emotional intelligence's superiority: "empathy".
I think that it would be interesting if those people were to be interviewed after their term is over; once they're off the job; would they admit, then, their achievements?