With the exception of a few outlying examples, no job being discussed in this article is a leader. A leader has followers, and he can convince them to follow him through his sheer force of will and inspirational ability. Examples of leaders: Barack Obama, Mahatma Gandhi, Charles Manson, Jaime Escalante, Joseph Smith, Napoleon, Steve Jobs, Elon Musk, Mao Zedong.
The people and job titles being discussed here are not leaders. They are managers. The difference is that people don't do what a manager says because he has inspired them to do so. People do what he says because they are paid to do so. That is, managers don't have followers. They have underlings.
Managers are of course needed. To work in groups effectively, a roughly fixed-arity hierarchy has many advantages, and in a hierarchy someone has to be a non-leaf node. The goal of a manager is to manage his underlings in such a way as to meet or optimize certain organizational goals. In general this is a very different set of skills than those found in the best leaders.
This isn't to say that certain leadership skills aren't helpful for management: obviously it's helpful if a manager can apply some powers of persuasion to his immediate underlings. But leadership skills are not necessary to management: there are plenty of reasonable managers with few or no apparent persuasive skills whatsoever (I'll be kind and not name names).
Persuasion is also not restricted to management: it's helpful in practically any job involving human relationships. This includes teachers, salespeople, hostage negotiators, lawyers, and magicians.
But few other career paths imagine themselves as "leaders". Teachers don't go to leadership seminars or buy ridiculous low-rigor books on leadership. This seems to be a cult special to the management community. Why do so many managers imagine themselves to be something they are not? I think it's for two reasons. First, they have power, and leaders have power, and so they have mistaken one for the other. Second, and more importantly, I think management is an awful and thankless life choice. Managers don't make anything or really contribute anything tangible to society. The Dilbert Principle is very valid here. And so managers try to imagine that their jobs ("leadership!") are more important than they really are, simply out of ego boosting.
I think that leadership is so valuable a skill, and so rare and powerful a force, that we should actively fight to prevent the management community from co-opting the term to describe the daily task of collating TPS reports.