You could easily define it this way. This would be valid. But for most of history it was unclear when a baby was conceived, so it would be silly for someone to say their baby was 9 months old when it was actually born at only 8.5 months. Days of conception similarly would not be a good substitute for birthdays because no one would know them. Then in general it was much easier to mark someone's age as when they came into the world as an independent being, and this tradition is far too entrenched (and simple and easy to handle and universal for people in poor countries etc) to think we would at all gain from now finding exactly the date of conception and counting age from that point.
