To your second point, one definition of leadership is "getting people to want to do what you want them to do." That's also a pretty reasonable definition, and the way to do that is by providing context.
I always ask 3 questions in my discussions:
What is the company's mission?
How is your team contributing to the mission?
How does the work you're doing today contribute to the mission?
If a leader, and everyone on their team, knows the answers to all three of those questions, at all times, then they will probably be very effective.