The answer to your question is this: Convenience.
1. Open the AirPods case, it connects automatically to all the Apple devices you have nearby.
2. You can choose the AirPods as a source in the AirPlay menu, like if I am listening to music on iPhone then I want to watch a movie in Apple TV while a toddler is sleeping, two clicks with the Siri Remote.
3. Someone is talking to you while you are listening to music, take it away and it pauses the music, put it back and it resumes.
4. With all the previous Bluetooth headsets I’ve used, the batteries is almost always dead when I need it, with the AirPods the case makes sure it is always ready when I need it.
5. The size of the case is perfect for any pocket.