I often hear people saying that making such things repairable would entail massive increases in complexity and less thinness/etc., but in this case it's relatively easy to imagine how Apple could have made the batteries in each AirPod replaceable (as for the charging case, that one is pretty trivial...) while maintaining the dimensions and weight:
This is a metal-cased cell, like an AAA battery, only smaller. They could simply make the "stem" of the AirPod unscrew from the top to access the battery. They came up with an unserviceable design because they didn't want to, not because they couldn't. Think of things like quartz watches too --- they have just as small if not smaller dimensions, and yet you can still replace the batteries in them. (And if you think threads of that size are impossible for Apple... look at the few screws that hold iPhones together.)
https://photos5.appleinsider.com/gallery/30055-49077-999-Air...
This is a metal-cased cell, like an AAA battery, only smaller. They could simply make the "stem" of the AirPod unscrew from the top to access the battery. They came up with an unserviceable design because they didn't want to, not because they couldn't. Think of things like quartz watches too --- they have just as small if not smaller dimensions, and yet you can still replace the batteries in them. (And if you think threads of that size are impossible for Apple... look at the few screws that hold iPhones together.)