Its a beautiful idea but the baby deserves the best care and a pediatrician is not sitting in the home with you waiting for you to deliver. The best thing for the baby is to have a staff of medical professionals at its beck and call and of course that goes for the mother as well. You never know what can happen at birth. Any type of complication can arise and for frum women the husband cannot assist and frum women do not have a score of mothers, mothers-in-law, sisters, friends, etc. along for the ride, in the home and in the room for the event!
So although the thought of it sounds more peaceful and calm, it won’t turn out to be that way if there is a problem.