At my last job I did data analytic work for the state's Medicaid and Medicare programs.
Since high cost childbirths can be extraordinarily expensive I had a few requests for ad-hoc work on the topic and had to do two more extensive analyses (including setting up a dataset for others to use).
I was given birth location/type as one of the possible targets and sure, if I focused on that and ignored the other factors I could end up with various arguments supporting one side or another. . . but the more I factored in other data points (demographic information, specific conditions, etc.) the less it seemed to matter in the grand scheme of things.
Instead things like 'how much access to healthcare did they have before the child was born' and 'did anybody even know who they were?' and 'did the mother have access to good nutrition at the beginning of pregnancy' were pretty much the strongest drivers . . .beating out classics like prior c-sections and high or low age bands by a significant margin.
Even after those were filtered out (because at the time the idea of making sure everybody was insured wasn't terribly popular with the new director) how/where the child was born was only a factor in emergency births (being birthed at the scene of a car accident), once we had the consistent care factored in it didn't seem to matter much what sort of care they got, just so people were paying attention.
I suspect that's why people aren't agreeing on this, because it doesn't matter terribly much and because we've advanced our technology enough that we can see the complications enough in advance.
Of course I'm not an obstetrician or anything, but I had some good people advising me and I'm pretty sure we didn't miss anything obvious.