Coming home from NZ just before Christmas on a massive plane packed with 600 souls including 200 children I was dreading it but though we had 3 calls during the flight asking for a doctor, not one was for a child. One was a drug overdose, another food poisoning. I was surprised that there wasn't an on board medic but apparently when someones sick or dies or has a baby, the cabin staff call HQ, in this case Arizona, where they are talked through the procedure but must have a doctor or nurse on board to sign it off.
My nurse DiL has volunteered a few times thinking she might be upgraded. Alas instead she spent one night with a distressed passenger who was going cold turkey.
Meanwhile on our flight, all the children slept peacefully.
So no, I don't think it would be economic or sensible to ban babies