I agree with Don about the headrests being a pain in the neck :lol: and suspect they're specifically designed to minimize head movement in the case of a rear-ender or maybe keep the head in a very-specifically defined location for the side airbag.
Marta - no you can't reverse them as only one side has the locking indentations (BTW, you've been lurking forever - are you getting an iMiEV?)
I only install the passengers' headrests if I actually have passengers - otherwise I leave them off to improve visibility.