FAT is still popular because it is very easy to implement, and anything can read and write to it. It is pretty easy to implement the file system on a low power microcontroller and have it write data to an SD card. Your users can then plug that SD card into any computer and view the data, or add to it.

Using btrfs in a situation like this means a lot more coding on your end, and your users lose the convenience of the SD card using a file system they can easily interact with.

Nobody is using FAT for their primary system partition. It is almost exclusively relegated to embedded systems and small external storage devices where broad compatibility is an important feature.