The problem with this thread, OP, is that it berates women for not perceiving risk correctly, which is exactly what a lot of the anti-home birth/anti-choice rhetoric berates women for too. That is why this thread was ill-advised.
The real problem with any conversation about risk in childbirth is that it based on the premise of low and high risk. These labels were originally developed for population-level health surveillance after WWII/start of the NHS, but are now inappropriately used to triage women or even to push them into 'birth plans' that they don't really want. And that goes in both directions.
That is why statements like: 'home birth isn't risky for people who are deemed to be low risk' can sound a bit hollow to many women, particuarly those who have given birth in recent years as maternity scandal after maternity scandal has emerged.
You are asking women to align themselves with a set of inappropriately used labels surrounding risk, which women know they will then be blamed for 'not understanding' when it all goes wrong.
I'm a scientist and the entire 'low risk' label is inherently unscientific. Low risk women are not monitored or rather 'observed' (though sometimes their babies are, though that is a whole 'nother thread!) so we are actually unable to learn exactly what a 'low risk' birth looks like from a scientific/mechanical/medical perspective, which would allow us to better predict when interventions may be necessary.
Compound that with the very poor experience many women have surrounding their reproductive health and actually, many of those 'low risk' women are just undiagnosed women. I believe my undiagnosed endometriosis had an impact on my 'low risk' birth in a way that remains unappreciated, for example.
You point to Denmark as a good example, and they are. I believe they have the lowest maternal and neonatal mortality rate in Europe if not the world? However, many of the 'home birth' crowd on this thread would not be thrilled with the 'compulsory' c-section for breech birth that medics there are proposing is adopted internationally to reduce maternal and neonatal births globally.
There is very little room for a conversation inviting the possibility of more home births and more elective c-sections in this country, yes partly due to funding, but also some quite nasty attitudes towards women, particuarly pregnant/labouring ones.
Similarly, all of the doctors/midwives on this thread talking about how 'unpredictable' births are. That is a manufactured situation developed through a refusal to observe 'low risk' births, and women's reproductive health in the first place. Proper research in place would make birth much less 'unpredictable' and we wouldn't be having silly arguments about inappropriately applied statistical labels.
Then how would the patriarchy function?