If the question isn't allowed, the defense lawyer will object and the judge will sustain. You are allowed to ask shitty questions as a lawyer, in fact you're encouraged. It's literally your job to make the other person look like shit.

You're acting like a) asking the question is a nearly criminal act and b) a pearls clutching person about to faint in shock. Criminal trial law is not a velvet glove situation. Both sides will make out the other to be scum. Don't be a wilting flower, that's a tricky way to trap a suspect, but not an illegal one.

If I have a chance to put someone in a position where I can ask a simple question and trust that their response to realizing that answering it will show the world that they are scum...I ask it. He can decline. His lawyer can object. The judge can direct the question to be withdrawn. That's the protection he has.

But if I'm that prosecutor and my read is that he doesn't think I know about the Facebook messages, and I think that surprising him with a question that reveals that I know he's screwed if those messages get out...then I'm going to ambush him. There's a ton of good reasons why that is a legit and useful tactic. Maybe I suspect he'll claim it's not his account and he didn't send them, so I want his reaction and fear at the discovery to be seen in public. That's a perfectly reasonable strategy.

He doesn't have to answer, and he doesn't have to be assumed guilty for looking over to his lawyer and asking "do I have to publicly reveal that for the record". But, if my job is to prosecute a person grooming an 11 year old, I'm taking zero chances and I'm going to nail him to the wall. That's not violating ethics, that's prosecution strategy. I'm hoping he turns pale, starts sweating, stammers out something unintelligible and starts panicking at the thought. I want people to see that this guy just realized that he's screwed, and I'll set up that gotcha to be as destructive as possible. Because the victim and his potential future victims deserve nothing less.