I think it's the case that a human baby's head is bigger in relation to its body and in relation to the opening from which it has to exit, than any other mammal.
If a woman is prepared to have her baby naturally then that's fine but I do believe that if it is something that really frightens her then she should have the choice of a C section.
Speaking personally, I was nervous of natural childbirth but not terrified. However, having had a very distressing induced and prlonged labour, being sewn up badly by a junior doctor and suffering from what I now recognise was post-natal depression with my first child, I decided against having any more. Seven years later I nevertheless continued with an unplanned pregnancy and subsequent induced labour which, though unpleasant, did not have such profound after-effects. My pregnancy was a time of fear and trepidation. Had I been given the opportunity to have a C section, I would have jumped at it, and I believe women should be informed of the risks and left to decide for themselves.
As to the idea that women in other countries who have no, or limited, access to medical care and interventions sail through through their labours without a care, I believe that is not borne out by the facts. My understanding is that a far larger number of these women and children suffer permanent physical damage and sometimes die.