Stats are good but simple logic is too. Many complications are rare but if add up all of them, the chance of having one is not so low. 1-2% chance is high. 3-4-5% is even worse.
Home has no OR or blood bank or extra people to help. There is not way around it. An ambulance takes longer than 10 minutes and no one know how to teleport patients yet.
The absence of technology at home is the reason why the stats are so bad.