Why would they?
Death in child birth, although rare in the first world, is natural death. Death by the pill is not.
The pill is touted as safe. I have never known anyone to assume that child birth is perfectly safe.
The pill is touted as safe? By whom? You may not know this, being a guy, but when a woman goes in to get a prescription for oral contraceptives she is presented with a list of side effects and contraindications as long as your arm. The pill containers come with lots of small print detailing the horrible things that can happen and warning you not to take it if you have any of the listed contraindications. There is no way you could walk away with those pills and not realize there is risk involved.
My Mother was always bugging me about the risks of taking the pill back in the 70's. She worked in a hospital.
I understood the risks, but discounted them. Thankfully, she never had to tell me "I told you so".
The more I see medications advertised on TV and hear their potential side effects, the more thankful I am not to be on anything! Their disclaimers scare the liver out of me.
No medicine is ever touted at 100% safe, with no side effects. Even OTC has a label full of warnings. Every time I went in for a checkup to refill BCPs, I had to answer questions - have you had any leg pain? headaches? blurred vision? etc etc.
Blood clots can even form during surgeries. When I had a relatively simple GYN procedure last year, I was given a list that was also gone over in detail with my H and I, of things to look out for. Leg pain with warmth and knotting was one of the first, a warning sign of a blood clot.