Managers fight tooth and nail to maintain the current condition, the status quo. They work to make sure that everything is done exactly the way it has "worked" in the past. You might hear (gulp) "that's the way we've always done it" (like that's a good thing).
Leaders constantly challenge EVERYTHING, and there are no sacred cows. Standard work means "how we ALL do the work and the best way as of today". In the companies I have the good fortune to work in, there have been hundreds of improvements made using A3 as the vehicle. A3 can be thought of as a great way to find out who your future leaders are.
To lead A3, you need to identify a problem, recruit a team of 3-5 of your peers, take them through the DMAIC while leveraging diversity and gaining agreement, and then teach everyone else what the team learned. A3 leaders don't solve the problem, they lead a team that solves the problem. Doesn't that sound like what great leaders do? At the end of the year, when you look at the A3 scorecard, look for the people who have led a dozen or more. In many cases, not only are those people pretty good at leading A3, but they are probably good leaders, period. Think of A3 as a constant audition for leadership. Once identified, these folks can be engaged to help others lead A3 and teach lean to people who haven't done it yet, or new employees.