By this means, the passenger can sleep ... and ... get a tiny bit of privacy since he can "bury" his eyes in the corner made by the headrest. His head won't fall over when he zonks out and his neighbor will not be bothered. And no one will see him drool.
Such a rest should be as big as is reasonably possible. It should be on both sides of the seat and it must snap into place easily and be reset just as easily.
I know this will work from personal experience on the "freaking" Greyhound bus ... perhaps the most miserable way to travel due to inability to sleep ... and ... constipation (but I don't know what to do about that other than a laxative).