Because, realistically IT IS a parenthood lawsuit waiting to happen. And at the end they will have NO ONE but themselves to blame for coming up with such a dumbass idea.
It tends to happen only very rarely. Most donors, especially donors who have taken time to consider it who have talked with the mother about what donating means and doesn't mean, tend to be okay with the arrangement as it plays out. Most of the cases where custody is sued for involve a male donor related to the non-gestational mother and the mothers having gone through a rough breakup. I'm not saying there's a 0% chance, but from the looks of their arrangement, it's not likely. In the US, it's a bit different, we used a donor from a sperm bank because my wife would be considered the second parent by default, that's not an option in Japan.