Per your own link:
“ Variations in caesarean section rates across countries have been attributed to a number of factors, including financial incentives, malpractice liability concerns, differences in the availability and training of midwives and nurses, and the proportion of women who access private maternity care. For example, there is evidence that private hospitals tend to perform more caesarean sections than public hospitals. In Switzerland, caesarean sections were found to be substantially higher in private clinics (41%) than in public hospitals (30.5%) (OFSP, 2013[1]).”
Per your own link: “ Variations in caesarean section rates across countries have been attributed to a number of factors, including financial incentives, malpractice liability concerns, differences in the availability and training of midwives and nurses, and the proportion of women who access private maternity care. For example, there is evidence that private hospitals tend to perform more caesarean sections than public hospitals. In Switzerland, caesarean sections were found to be substantially higher in private clinics (41%) than in public hospitals (30.5%) (OFSP, 2013[1]).”
Privatization correlates to more C-Sections.