I think there is a difference between having a relationhip with an OB (through the private system) that you have chosen and you trust to do the right thing when it is game time, versus having your child delivered by someone you have never met before within the public system.

I would also prefer to be cut, with or without my informed consent, if it meant having a healthy child born alive at the end.
I imagine most HCP would see that as their end goal and would assume, rightly or wrongly, that most women would too.