I can think of lots of reasons why the bio-offspring would not be named in an obit, and only one of them is spite toward them on the widow(er)'s part.
It could be that the deceased himself, or the bio-offspring themselves, didn't want the names mentioned. This could be either because of a nasty, acrimonious estrangement, or a case of the bio-parent graciously stepping aside to let ex's new spouse raise the kids as mom/dad -- with or without legally terminating parental rights.
Or it could be the widow(er) tailoring the obit to the local paper's readership -- who don't have any connection to the deceased's bio-kids, so their names aren't relevant.
I worked at small-town newspapers in the 1980s/early '90s, and we ran obituaries-as-news-stories on everyone local who died, unlike big-city papers who only ran them on prominent people. But because they were free, they were very formulaic: Only immediate family members got named. So if you were the longtime live-in lover of the deceased, or the grandniece who lived with him and cared for him in his last years, you would not be mentioned by name in the obit.
These days, those same papers charge for obits, but people can write whatever they want, and name (or not name) whomever they want. I like that better, even if (a) it costs money, and (b) some people might get slighted by the family members writing the obit. People got slighted back in the days of free obits -- it was just the paper's call back then, and not the family's.