No, they are managers; management and leadership are different things. Being a manager is a set of things that a person is authorized to do on behalf on their employer, "hire, command work and fire" as you said being examples. Leaders nurture their staff so that they work together effectively as a team to achieve goals. Very few managers are good leaders.

there’s space for both perspectives.

they are not “leaders” in the purest sense - they don’t demonstrate characteristics of leading, but rather characteristics of people who strive for power and influence.

yet i also get that, in spite of the deficit of true leadership skills, they still guide the group into a specific direction for better or worse.

Those are "executives"

Bosses are those who hire and fire. Leaders are those who other people willingly follow.