I personally would have been a bit 
if someone had given me a present from my LO when he was a newborn but I can't see that it really does any harm either if it makes the parents happy.
But actually, not long after LO was born it was Mother's Day, and DH did give me a present and card from him and I did it back for Father's Day. It was nice, and because of our previous losses it made it special to finally be able to celebrate the days as parents, even knowing full well that LO had nothing to do with the choosing, shopping for, writing on or wrapping any of the cards and presents.
But the Mother's Day I'm really looking forward to is the first time LO comes home from school with a card he made himself. 
DH also gave me a ring when LO was born, but again I think it was more special than a 'push present' for the sake of it. It had been a difficult pregnancy requiring lots of examinations, operations, injections, bed rest and worry. My previous pregnancies had always ended with the loss of our baby and the births taking place with us knowing our baby had died or was going to die very shortly afterwards. I'd been very ill and almost died during the birth of our daughter and our marriage had been strained to breaking point with the grief and outside stresses placed on us following the losses.
Yet we came through, we were still together and we'd finally had the baby we longed for and were a 'proper' family. That would have been enough for anyone but DH said he wanted to get me something special that had personal meaning to us and all three of our babies. The ring means the world to me because of all it stands for personally, from the reasons DH had when he went out and bought it to the memories it brings back to me when I look at it.