I had a home birth with my first (5 years ago) and planning another home birth with my 2nd now. It was lovely. I really can't quite get my head around birthing in a hospital. I think it's absolutely necessary when there is a medical need and I'm fortunate I've never had a medical need to, but it seems inconvenient and scary and painful. I found being at home I was really relaxed and comfortable. I didn't find giving birth painful. I think because I was so relaxed. I didn't need any pain relief really, just used a TENS machine. It was so nice being able to just be in my own space, not rushing around everywhere. My daughter did need to be in hospital when she was a week old (totally unrelated to her birth, she had some feeding issues and lost a lot of weight) and it was a nightmare. I found it so stressful. Nurses and midwives coming at all hours. As soon as I started to fall asleep, some siren would go off for an emergency and like 20 people would run down the hall with carts in a panic. I couldn't even sleep there. I couldn't have imagined wanting to give birth there if I'd had another choice.
I too live about 10-15 minutes from the hospital and I feel really comfortable with that. Realistically, in an emergency, it takes 10-15 minutes to respond even in hospital if you need a high level of care. If you needed an emergency c-section, there are consent forms to sign, you need a spinal or to go under GA, they'll need to put an IV in you, the operating theatre needs to be cleared and sterilised from the previous patient, etc. All of that takes time and you will very likely be waiting 10-20 minutes at the least to get in. The home birth midwives in the UK (it's not the same in other places) are very well trained. They have all the same tools that hospital midwives have, except they can't do a c-section. They can deal with a breech baby, shoulder dystocia, a baby who needs oxygen, excessive bleeding, a retained placenta, etc. They also err on the side of caution and will recommend a transfer in situations where if you were in hospital they'd just leave you another 20 minutes and check again later to see if the problem is still there. If you do need emergency care, all that will be prepped during your transfer, you'll do the consent forms, etc. so you shouldn't wait any longer than if you were in hospital (unless you live like an hour away).
That isn't to say there aren't poor outcomes sometimes, but those same things happen in hospital too unfortunately and it's rare for them to be connected to home birth per se. I have a family member who had a baby with cerebral palsy because of oxygen deprivation. She had a consultant led birth in hospital. I know another who unfortunately lost her baby due to inappropriate use of forceps, which caused spinal damage. Medical mistakes happen, but they happen every where. Fortunately, you're much less likely to need too much intervention at home so likely to avoid many of the opportunities where they could come up. I feel very strongly that I would have had a very different birth with my first had I not been at home. I had a long 2nd stage (4 hours of pushing) for no reason other than she had been back to back and it took awhile for her to turn. I was fine, she was fine. The midwives paid very close attention to my BP and her heart rate and there were never any concerns that all wasn't going just fine. In hospital, usually the cut off is 2 hours for your first and they go for an instrumental delivery (forceps or ventouse). My friend (different friend than above) had a horrible experience with a forceps birth and her son had awful bruising and cuts to his face from it. Obviously, when you need help, you need help. But I didn't (my daughter came very quickly when she was turned into position and ready and overall it was a lovely and otherwise quick birth) and I think if I had been in hospital, it would have been a very different experience for us and probably quite traumatic. It fact, it was lovely and very calm and peaceful, and I'm really glad that's what we planned.