I assumed that he wasn't in the mother's (or child's) life except for the child support payments link, and therefore planned on her believing him to be dead.
If he was still living near her or even in contact with her then yes, it would seem to be a completely pointless plan to me also.
I thought the same. As ever, most of these people seem to get caught because they get greedy (possibly I've been listening to too many episodes of Darknet Diaries recently).
Think so? At some point you'd assume the other parent would be pushing for the payments through some avenue that would lead them to tell her that he's dead.