The fact that nothing can be done about the situation is the precise reason nothing should be said, or a white lie presented.
It’s the reason we don’t send out a text or email saying your bag missed the flight until AFTER you land. We aren’t turning the airplane around for it, and we don’t want you to dwell on that issue for 2+ hours with no means to talk to customer service.
“There was traffic on the runway ahead of us and we had to do a go around” is a perfectly acceptable lie instead of “sorry folks, we lined up for the wrong runway. We’ll get it right next time”.
Circling the sky in a pressurized metal tube requires cooperation and calmness from all onboard. Some info doesn’t need to make it into the cabin.
The problem is that now I know that pilots are easily capable of lying and will panic no matter what they say. Because they could easily be lying.
How am I supposed to trust someone who instead of admitting a mistake, lies to my face? Especially since we all make mistakes, and aviation is safe specifically because mistakes are openly admitted, analyzed without blame and prevented in the future. OK, don't make the passengers worry. But don't lie!
That's why you can possibly omit information (because yes, passenger calmness is important), but lying should never be attempted, as that just creates mistrust in the future.
As for the bags example, if I know ahead of time that it didn't make the flight, I can use onboard wifi to order the things I need. Instead of scrambling to look for them at the last minute. Or after the time for same day delivery of shopping has passed.