I'm no medical expert, but this is what it seems to me
* The chances your baby will use his / her own cord blood is very rare
* The chances that a large pool of cord blood / stem cells can help sick children in general is very good.
So, in a broad societal sense, it makes sense for everyone to donate their stem cells into a large collection, and then for those cells to be sorted and matched to those who need it. It's like a numbers game.
Of course, some people like to take every precaution, in case their baby gets some very rare illness.
But I think there is much fearmongering out there. My first ob/gyn (who I got rid of) tried to tell me I was "high risk" and had a chance for an etopic pregnancy combined with a twin pregnancy. When I looked it up online, there was only a 1/10,000 chance of this happening, and I had none of the symptoms. So he was clearly just out to sell me services I had a 9,999/10,000 chance of not needing.