While that may be true, it's a red herring. The logic does not mean that women in childbirth are sick - more specifically, it does not mean that women in childbirth need intervention.
I think regardless of how we label things childbirth is a risky business and many of the risks can be reduced, even the UN has recognised that as countries caesarian rates increase up to around 10% there are significant reductions in mortality, after that point the advantages in terms of mortality are less obvious. Its really a risk management decision informed by the woman's personal choice.
No. The reason for the greatly reduced risk is much more due to the subsequent establishment of the Germ Theory of Disease. In the early 1800's, most practices knew little of sterilization and contamination.
Actually Pasteur cultured the streptococcus early in the 1800's and Lister was introducing the principles of asepsis a little later, this was largely ignored in the world of obstetrics, it wasn't until 1929 that the Royal College of Obstetricians recommended surgical gloves and masks during deliveries. While this did have an impact, it was less than what many people believe, it wasn't until the introduction of drugs that puerperal fever, the major killer was conquered.
Annual death rates per 1000 total births from puerperal fever in England and Wales (1911-1945) (Registrar General Reports)
Because formula is definitely not adequate.
The response to the breast feeding point is interesting, its certainly true that there are advantages but the reality is is that these advantages are only really seen in the developing world, at a population level in the west it is very difficult to demonstrate significant health advantages.
It is not however difficult to identify the harm being done by the uncritical promotion of breast feeding and the negative moral judgements that accompany it with the guilt and disapproval of formula feeding leading to double the rate of depression.
The National Childbirth trust has been critical of this saying that women can experience unacceptable levels of pressure and the Royal College of Midwives this year issued a position statement reaffirming a woman's right to choose and stating explicitly that women should be supported if,... they opt to bottle feed using formula milk.
This article is fairly typical of what is increasingly seen in the media and links to supporting evidence.
https://www.telegraph.co.uk/women/mother-tongue/10911177/Breastfeeding-wars-is-breast-really-best.html
I would also say that you misrepresent much of the research. When comparing the outcomes stopping at the point of delivery would be daft, and in fact most of the comparisons are clearly in relation to longer term interventions, I don't remember if I posted this link to the latest care pathway which links to all the underpinning work but it is informative, you just click on the various sections. Somewhere in there was the point that 4 c-sections are not associated with increased risk.
https://pathways.nice.org.uk/pathways/caesarean-section#path=view%3A/pathways/caesarean-section/deciding-whether-to-offer-caesarean-section.xml&content=view-index
You might be interested in reading some stuff about the inquiry into midwifery services the Morecambe Bay Trust which identified the
midwives role in pursuing normal childbirth at any cost and the consequences of this, though there were lots of other issues involved. It provides a useful overview of the relative roles and power of different organisations in relation to the law and its findings were damning leading to some very serious consequences.