When they're on duty, though, they are acting in the service of the public, not as private citizens. We need to be very careful about letting them have much or any privacy while they're at work. There's just too much opportunity for abuse.

No, I don't think this is unfair. It's certainly no less unfair than when restaurants like Chipotle and Steak n Shake use open kitchens. Having employees do their work in full view of the customers is not very different from requiring police to use body cameras from a privacy-at-work perspective, and is done for much the same reason.