Take a look at the front and back of the Airpod flexible circuit board, there is pretty much no room for anything else. Even the smallest nand flash chips take up more room than the circuit board can offer. The airpod case has more room in it, maybe there could be a storage chip added to that for on the go music (like an ipod shuffle!) but Apple would probably just rather you buy a watch.
iFixit photos: https://d3nevzfk7ii3be.cloudfront.net/igi/XwBdUPqAmhHbWgWn.h... https://d3nevzfk7ii3be.cloudfront.net/igi/1ZnAZMJBfmIxFr1f.h...