I saw this thread and came to post, but it looks like Joseph said a lot of what needed to be said. Just because people have a lot of intermarriages, and a lot of non-halachic kids, doesn’t mean they’re raising those kids Jewish. Of those who are raised Jewish and aren’t halachic, they will most likely go on to marry goyim and not raise their kids Jewish. The odds of a family line descending from an intermarriage and continuing for long enough for it to be ambiguous are extremely slim.
There’s another question of how many halachic Jews are out there being raised as Christians. The woman tends to get her way when it comes to the religion of the kids in all corners of society, so hopefully this doesn’t often happen.