Hospital births are risky too.
Oh, certainly, nothing is risk-FREE. So the question is, are hospital births AS risky as home births for moms and babies of comparable inherent risks? IOW, is a breech baby or a set of twins or a low-risk full-term head-down singleton as likely to come out of a hospital birth alive and well as they are out of a home birth? And how about the moms?
And the studies, at least in the US, seem to say no, they're not. Hospital births are not without any risk, but they are LESS risky.
AFAI have seen, medical staff only allow home births for those who are low risk, and there is always some risk in having a baby.
What country are you in? In the US medical staff have zero input on whether you do a home birth. If you can find a midwife willing to do a home birth--and there are non-CNM's out there who will agree to home births for 43-week breech babies, monoamniotic twins, and other high-risk births, no problem--you can do a home birth.
Of course, the midwives willing to do this generally have no medical training (they're not CNM's), upping the risk still further ...
There's risk to surgery and also to being put to sleep during surgery.
C-sections are usually not done under general anesthesia--just a heavy epidural or spinal block--so the risk of "being put to sleep" isn't there.
Ironically, the moms who end up needing general anesthesia for their c-sections are typically the natural birth/no drugs/no interventions ones, including the emergency transfers from home births and birth centers. Reason being that:
(1) they don't have an epidural, even a light "walking epidural," so the option of just upping the dose of meds in their epidural isn't there--it takes 30-40 minutes to get an epidural placed and have to start working, which is time you don't have in an emergency (general anesthesia, in contrast, works almost immediately); and
(2) they are more likely to reject interventions (or not even be at the hospital) until the situation becomes life threatening, so by the time they consent to a c-section there is no time left to wait for an epidural or spinal block.