Pat:
Nobody here is defending these songs on any grounds of quality or taste. They are offensive and disgusting. That is why no one wants to sing them at funerals, counselling sessons or to grieving relatives.
What is interesting, is why they exist at all. They certainly shock, because of their callousness and insensitivity. I would argue that this insensitivity is essentially bravado. It is faked. It is the same sort of bravado as the WWI soldiers who sang:
"If you want to find the regiment
I know where they are
They're hanging on the old barbed wire."
This sort of humour is known among policemen, servicemen and medical staff. My cousin, a nurse on an infant intensive care ward, used to joke very vulgarly about the fate of little babies suffering. Believe me, I would have trusted my cousin to look after my children, because she cared about children very much. She suffered a nervous breakdown after a series of children had died in her ward. I would never have joked vulgarly about children's illness in her presence, but the sick humour was her way of dealing with it.
I don't expect you to change your mind, because any decent man would be moved by the fate of friends grieving for a baby. I would just respectfully say, that for some people, who have to deal with this sort of awfulness on a regular basis, this is one of the defensive mechanisms which they choose.