But I may be close enough to one of the kids that I'd like the opportunity to give my condolences, and yet still not close enough to be in immediate contact with them.
And I can easily still not know their father's name.
To me it's just a matter of completeness, not even of "ooh, he was estranged from his kids." It's bad form to leave out names of a person's direct children in this situation. Grandkids, sure, but names of first-degree relatives should be given.