The better job you do of managing the easier your job becomes.
As a manager your primary responsibility is to improve the system: both the systems within your sphere of control and those outside of it. The more effectively you do so, the less firefighting you have to do. The less firefighting the less hectic and chaotic your days are. And the more time you have to focus on improving the system.
The better you are at leveraging your efforts, the greater your impact, and more quickly your job gets easier. Most effective leveraging involves improving the system. Improvement to the system continue to deliver benefits continuously.
A specific form improving the system is coaching people so they are able to be more effective at improving the system themselves. One valuable role you can play is to help avoid the existing traps that prevent improvements. Early in a transformation to a continual improvement culture there are significant barriers to improvements. Those not only prevent the system from improving rapidly they can easily derail the motivation people have to improve. It is hard to maintain a desire to improve if every effort to do so feels like a long slog through quicksand.
As you create a system where people have the knowledge, drive and freedom to improve you get to enjoy continual improvement without any direct action by you. As this happens you are able to spend more time thinking and learning and less time reacting. That time allows you to find key leverage points to continue the progress on improving the management system.