The rule is a power trip, plain and simple. It gives CBP (or whatever they call themselves these days) the ability to control passengers' access to information, and to threaten/intimidate them if they violate the rules. Limiting access to information makes sheeple more compliant. It reduces accountability for the CBP employees because they can't be filmed or have their actions reported first-hand in real time which aides their ability to act with impunity.

As for why people get annoyed, IMO law-enforcement types and their apologists often become annoyed when the power-tripping nature of so many of their actions is pointed out. If you get these people to talk honestly (maybe after a few beers), many would say they wish cell phone and cameras banned outright. How many times have cops been caught in public places (illegally) trying to confiscate cameras from bystanders, force people to stop filming, or using a wall of cops or police horses to block public view of their actions? How often are police punished for this behavior? (answer: rarely if ever)

I'm sure that at some point in the distant past there was an articulable reason for the no camera/phone rule, though it may have been a local/special case. In an era where high-quality cameras and phones were not ubiquitous, someone possibly surveilling the immigration/customs hall and passing on information to an associate via a phone or 2-way radio probably seemed genuinely suspicious. But then it got morphed into a way to exercise power over the people, as so many things do.

As with most power tripping rules, the people who are hurt the most are law-abiding innocents. Any credible criminal would use hidden cameras, earpieces, and/or texting under their coat or in their pocket, to conceal their activity. But your average traveler trying to rebook a flight or warn his ride that he's late gets yelled at and screwed.

One of the key ways to know that a policy is a power trip is that you can never get a straight answer as to the purpose or that the answers make no logical sense. I've heard everything from "you could use your phone to detonate a bomb in your checked luggage" (you could also use a pocket detonation switch, or use the phone while still on the plane, have an accomplice not on the plane who performs the deed after he sees the plane land, etc.) to "you could steer a drug-carrying accomplice away from dogs or other law-enforcement operations" (which could also be accomplished using a messenger, or hand signals, or many other means) to other nonsense answers or the total inability to answer. I've never observed or heard of an airline enforcing this silly rule on their aircraft either. They will announce that you can't use your phone in the arrivals hall but have no problems with using it during taxi in, or before deplaning during the era when taxi-in phone use was disallowed.

I would have no problem with a rule restricting casual camera/phone use when actually at the passport-control desk or interacting with customs, primarily because it's rude to delay those behind you, but also because that's where any sensitive information might be. Or with extending that rule to the first 3 or so people at the head of the queue.

But everything else is a power trip.