Having one "leader" that you roll all the executive functions or skills of power into, and who just does all those things while a bunch of "followers" do none of those things, is imbalanced and vulnerable.

If you have 1 leader, the government or counter-revolutionaries can easily assassinate, incapacitate, blackmail, bribe, or compromise that leader, and you can kiss your progress goodbye. If you have a council of the highest roles in different domains that are distributed amongst several people, it's much harder to compromise, the payoff is less, and a compromised figure is almost automatically replaced.

But is that really one unitary thing, or is it like the concept of intelligence, where there are a lot of different measurable capacities that all get rolled into one, and we think about it as one single concept because we are accustomed to using the word for that concept?

I'd be willing to bet those boards also had a "secretary" and a "vp/co-chair" and a "treasurer" and possibly other positions, because "the one person who runs everything in the organization" is both too much for one person to handle, and doesn't allow people to specialize as well.

You have described a "leader" as a Social Connector, a Conflict Resolver, a Parliamentarian, and a Generalist. Why should these all be one person, instead of separate people, so they can all do a better job of their thing?

they think that their job is to just be assertive and motivate the other members to do their tasks, which is what the media often describes as ‘good leadership’.

Sounds like there are many divergent and incompatible definitions of "leader" and "leadership".

Thinking about the Cabinet of the executive branch also informs my thinking. Joe Biden is a perfect example of how all the departments would run just fine without him. Yet he is the foremost leader in the land.