It's an interesting idea for a study, but there would be problems carrying it out. Neonatal death is sufficiently rare that you would probably need thousands of participants in order to have a reasonable probability of detecting a statistically significant (meaning not likely to be due to chance) difference between groups. I think you'd have some problems matching up the two populations as well.

To add on to your point, though, obstetricians do way more cesarean surgeries on average than are necessary, and we have data that cesarean surgeries are associated with increased risk of perinatal death in the current and future pregnancies. It must logically follow, as it does in your "more preterm deliveries" argument, that those avoidable cesareans lead to some number of excess perinatal deaths, if not in the original pregnancy then in subsequent ones.

-- Henci