It is not fair to have a conversation in which it is assumed that the risks of home birth are the same as those of hospital birth, and that therefore proximity to hospital is the crucial or deciding factor in safety.
The risks of home birth are a different set of risks to those of hospital birth. You can not compare them. There are problems with birth and the surrounding processes that are caused by the environment of hospital, procedures of hospital, medications given in hospital, entry exams to gain admittance to hospital, hospital based infections, iatrogenic complications - these risks for a second birth are largely taken on by the mother - she is more likely to come out of the birth with injury than she would have been at home. The first intervention is to decide to leave the home and sit in a car, then enter and unfamiliar environment with strangers, lights, sounds. This is especially true of fast labours, when journeys like this are often undertaken in late stages, and women are risking giving birth en route.
I am not going to be the person who lists dangers of different types of birth, because this is a conversation with a pregnant woman. I merely want to point out that there are risks of having a baby in the hospital that you do not encounter when having a baby at home. And there are risks of having a baby at home that you do not encounter in the hospital. But both sets are vastly different, and only the person giving birth can possibly decide which they find preferable. Only them and not one single other person - partners, husbands, wives, parents, midwives, doctors, nobody else gets to choose.
And for the record, the home vs hospital birth rate for the HCP I know personally is about 50/50. As you’d probably expect when speaking about two very safe choices.