well also too i think it would cost too much.
This information is already gathered. They already know it.

You should see the amount of paperwork that is done after a birth. I was at a birth a couple of days ago where the mother was standing against the bed pushing, the midwife was sitting on a footstool behind her waiting to catch the baby and filling in the paperwork in between pushes! Anyone who has gotten a full copy of their labour notes can attest to the information they collect for the hospitals purposes.

Releasing this information would not involve any significant additional cost whatsoever.