It's not enough to just show up to class and lead a workout. That's not leadership and I'll tell you why--because any monkey can do it without too much trouble. I can point to damn near any student and say "handle the warm up" and guess what? They will handle it. If push came to shove, let me tell you something else, most competent students could coach the whole session without too many problems.
Something I have learned over the years is that leadership does not automatically arrive with a new belt, in the case of belted martial arts, or a recent fight, in the case of sports combatives. Leadership is one of those things that some embrace, but most don't; even when forced into leadership roles, the majority will fumble with the social dynamics necessary to make it work.
Being a leader is a 360 degree endeavor and requires more than simply showing up, though that's a pretty important piece of the puzzle. Consistency is valuable. But there are also key elements that need to be included. Things like demonstrated values, a grasp of scope, an eye for details, and the ability to externalize concepts that have been internalized.
Communication, understanding the difference between empathy and sympathy (and when one is appropriate when the other is not), problem solving, and a focus on making people better are just a few other things. The list is hardly exhaustive, but you get the point; there are some lofty requirements to leading.
Without those, you're not a leader; you're, at best, just the person in charge. And take it from someone who spent over a decade in a career that desperately needed leaders, but only had people "in charge," that's not enough. It definitely won't be enough to retain students, inspire new coaches or foster mentoring--it will just be enough to keep a business afloat and that's about it.
When a student doesn't get the belt they think they "deserve," it will take leadership. When a fighter loses a fight, it will take leadership. When competitions don't go as planned, it will take leadership. When someone gets injured, it will take leadership.
Someone will need to be in charge, too; but if that's all there is, it's not much at all.
And students deserve better than that.