There is a reason that coaching is now seen as a core competency of leaders. The Core Competencies of a coach are skills that serve leaders well. To simplify, during coaching certification, people skills, communication skills, thinking, motivation, goal setting, and planning are developed. To build on that, consider this table with the 8 Core Competencies of a coach and notes on how they add value:
When you go further and read the full text of the Core Competencies of a coach at https://coachfederation.org/core-competencies, the power of coaching as a skill for leaders is even more obvious.
Great leaders are the ones that care about others and believe in their abilities. Coach training supports becoming a great leader.