I had a shoulder dystocia with ds1. He was born with an Apgar score of 1 (dark blue) and had to be resuscitated. It was 8 min between when they declared it as a shoulder dytocia and resuscitation which took a minute or two I think. They had to do the Alexander technique thing with my knees up by my ears and 2 people pushing on my stomach. Crash team and paed in to resuscitate him. Luckily, and amazingly, after 5 days in special care he is seemingly unaffected and is a normal 9y old now. I had been very keen for a natural, water birth during the pregnancy. I was really pissed off that they would not let me have one due to high blood pressure at the end of the pg. In hindsight, he possibly wouldn't have lived if the shoulder dystocia had happened while I was in the pool. Or maybe he wouldn't have got stuck if I'd been in the pool, who knows? The crash team were also just outside the room in the medical ward, wheras they wouldn't have been if I'd been in the MLU on a different floor.
Anyway, with my second and third pg we decided wherever I gave birth would have to have a resuscitaire in the room. This meant medical ward again unfortunately. I was reasonably confident it wouldn't happen again but my DP was so traumatised by watching ds1 being born, effectively, dead that he really wouldn't entertain a MLU or water birth for ds2. I felt I had to go with this really as he had been much more aware of how close we came to losing ds1 and actually saw it all unfold (wheras I was a bit out of it by then). In the event, ds2 was a quick and easy birth in the medical ward, no issues.
With ds3, I was again tempted by the MLU but with a previous shoulder dystocia and high BP at the end of all 3 pg I pretty much gave up on pushing for it as they were very opposed. In the event, I had a mild shoulder dystocia with ds3 (he is very similar to ds1 so I think it is something about their big heads!) but because they knew about the first one, the mw had called in a senior mw as soon as it started going pear shaped again and he manually manipulated him and turned him so he wasn't stuck for very long.
I managed to have a natural birth with all 3 with just gas and air and TENS, even in the medical wards and, in hindsight, 3 healthy children was all that mattered really.
Long story short, probably not worth the risk imo. MLU yes, home birth no, for me. I just couldn't get beyond the fact that ds1 would probably have died if I'd been at home. Everyone has to make their own assessment of risk though.