I still don't think there was any good reason not to break it to them in private first.

In a perfect world, I completely agree.

In a real world, I can see that McGonagall did not have time before breakfast to talk to all of the orphaned children. I can also see that she might strongly prefer to quench the early rumors and avoid starting new rumors by calling a number of students into her office. (Delegating it to Snape, the Head of Slytherin House, was not an option; and delegating it to any other teacher would have sent a signal of McGonagall not caring enough to do it herself, making this a non-option, too.)

Given all this, I still think she should have delayed the announcement to talk to the children beforehand; but I don’t think it’s a simple choice for her.