I think part of reason people feel this way about cops in particular sometimes is that a lot of their job is to go around monitoring things. It is hard to detect if they are actually working hard or not. Crimes are rare and noisy. If a doctor spends all day playing on their phone, the patients will notice. If a cop does—it was just a low crime day, maybe.

Also the general public has more opinions about the behavior of governments employees.

I dunno how to actually feel about this, from a “is it good” point of view. But I can see why people feel this way at least.

Cops need to be ready for shit to go down at any moment. They should be fully aware of their surroundings at all times. Firefighters, and those other professions you mentioned, when they're working, don't have the luxury of looking at their phones.

If you're a cop and you're on duty in a nyc subway station, your eyes should be on the people around you, not your screen.

My wife and I are both doctors; she does not carry her phone into her clinic rooms unless she's on call. I'm an anesthesiologist, so I have to be immediately available while I'm at work or on call. I always apologize to patients if I have to do more than glance at a text/call to determine if it's right-now important or can wait.