The Chantry raises all the children produced by mages, so they still have access to anything they would if in the Circle minus their parents.
And Thedas doesn't know much about anatomy due to the study being illegal since people think it will be used by blood mages, so I doubt they know the benefits that we do now.
Not every chantry is right next door to a circle tower. Given how isolated some circle towers are and how spread out the chantry's can be do you believe they'd summon a healer each time the child became ill? If the child was in the circle tower a healer could be literally within ear shot or already holding the child if the mother or father is a healer. It could take days for the message that the child is sick to reach the tower and by then he or she could already be dead.
Would they even call for a healer? We're talking about a culture that fears magic and the chantry encourages that fear. Why summon the mother or father to heal the child when there is someone in town claiming that they just need to drain the "bad" blood out with leeches. There is also the cost to consider after all. The parents or a friend of the parents would likely be willing to heal the child for free. A mage being summoned to leave the tower to go heal a child of unknown origins. What's the going rate for that?
If they know the benefits are not isn't the point. The point was that by separating the child from its mother they're depriving the child of the benefits and increases it's likelihood of death or developing improperly. That they don't know about such benefits only makes it even more likely that they'll harm the child.