Not necessarily. A humane call with, "Please don't discuss this until 4 pm, as I want to tell people personally" would go a long way. And if people do talk about it, you can still have the rest of the discussion, which is not just about revealing facts.

This is equally true for in-person layoffs done as individual meetings, which happen all the time.

True, but they can try to make both the recently laid off and soon-to-be-laid-off employees be too busy to communicate, or they can round up the ones who will be staying so at least they don't pass around the news to those who aren't going to be laid off before they know they're not on the chopping block.

In a remote layoff situation? The whole company would know the moment one person was laid off.

No, in an in-person layoff situation. I was addressing the comment I replied to where it said "This is equally true for in-person layoffs".

I've been in an office during an in-person layoff situation (surprisingly only once during my 15+ year career), and they were definitely taking advantage of it being done in person.

What potential problems could this cause?

Maybe a disgruntled employee takes down your database or copies confidential info onto their personal computer

Your notion is that nobody who has ever been laid off had a idea it was coming? And you want to build your security with that foundation?

No.

In that case I don't think your previous comment makes much sense.