As soon as the baby and placenta are out, it's too late to avoid injury during childbirth. It is no longer possible to let pain be guidance for minimization of injury. The chance was missed.
Have you seen a childbirth, and one without an epidural? There's so much pain that it's not going to be guiding anything. Physicians monitor the status of the infant via fetal heart rate monitoring and monitor the progression of the delivery.
I have seen more than a childbirth. I have 12 kids.
The most miserable and painful birth was in a hospital. That birth featured pain medication, fetal heart rate monitoring, beeping machines, and a prison-like situation with doors that locked us in. My wife was in pain for months afterward. We learned our lesson and didn't do another hospital birth.
The other 11 births were definitely not "so much pain", but pain did guide my wife to be careful. She was always up and about right afterward, without pain. One time she walked around town doing errands the next day.