Is moving data between computers that way a thing that non-technical people do often? FAT-formatted USB sticks seem to be good enough for that, but e-mail/Dropbox/file sharing/cloud sharing/AirDrop have much better UX for the average person.
Yes, it is a thing people do. The problem is, those non-technical people do not understand on-disk formats. (Nowadays, most USB sticks come preformatted as ExFAT.) There are also offline and low bandwidth situations. In healthcare it's common too thanks to HIPAA and nervous hospitals: let's say a patient wants to transfer a set of MRI or CT scan images/videos (typically provided on CD or DVD, in which case it's ISO9660, but sometimes USB stick - hopefully ExFAT but sometimes worse).