Bill, I can name some 3rd cousins, but not many. I know I can name far fewer than I have!

The ones I know are Kathy and Keith. And my children have met THEIR children, all 4th cousins. But it is rare these days. It takes a lot of work to hold a family together.
But Mormons can’t truthfully claim to be any better. Despite all their emphasis on family and historical records of their ancestors, they’re just as good as the rest of us (meaning, not so good) at being aware of their more distant relations in the present day.
Just as an example, I once worked with a local Mormon group on a theatrical production where we solicited, as part of that production, family trees that linked their family back to a “Mormon Pioneer”. The point was to dedicate the theatrical production to those persons who were the real pioneers as opposed to the fictional ones portrayed in the show.
An unexpected side effect of our solicitation of these names was that we introduced 3rd, 4th & 5th cousins to eachother, people who may have known eachother, but were never previously aware that they were related. I was the one that compiled the names for the program so I was the one that introduced the various cousins to eachother so I know for a fact that this happened.