A homebirth isn't as dangerous as people think. Yes, complications can occur and interventions become necessary but it's extremely rare for that to happen without plenty of warning to the midwife. Even something as dangerous (potentially fatal) as a cord prolapse (which means the cord has appeared before the baby and will become constricted during the second stage, depriving the baby of oxygen) but in this case the mw would ring an ambulance, and have her hand up you to hold the baby's head up into the uterus until you can get to theatre - a marvellous sight for the neighbours, I'm sure.
Even in hospital it can take 15 minutes to prep for theatre for which you'd wait. If you were being blue lighted to the hospital from a homebirth all that prepping will be going on while you are en route. In other words, you may not lose any time at all.
Midwives can generally spot a potential problem even an hour ahead, so even an emergency c section will have had plenty of signals.
I had an intervention-heavy first birth an ended up in theatre but it was plain quite early on that things weren't going well. I knew an hour beforehand that forceps were looking likely. Had I not already been at the hospital I'd have just transferred.
My second birth was so easy I wish I'd had a hb but the trauma of my first experience had put me off.
Considering a hb this time around, though.