That's an interesting question and I've never considered it, perhaps because after my two labors (short/intense/very painful and precipitous/ridiculously intense/horrendously painful) I know that if I'm already to the point where I'm almost pushing #1. it's too late to go to the hospital anyway and #2. there is no way in hell someone is getting me into a car. However, I can tell you why I'm not interested in UC, even after having a home birth during which the midwife was only present for the last ten minutes of pushing (out of a total of maybe 15 or something). For me, while I'm perfectly capable of learning what I need to know to do it completely alone, I don't want
to do it completely alone.
DD1 had the cord wrapped around her neck three times. It didn't cause any problems at all, but the midwife (CNM at a hospital) had to loop it up over her head for me to push her out safely. Not a big deal at all, but not something I want to have to think about unless absolutely necessary. I was prepared for this possibility at DD2's home birth, especially once we realized that, due to a precipitous labor and a road block we didn't know about, our midwife really might not make it on time, but I just didn't want to have to deal with it. I wanted someone else to notice those kinds of things so that I could concentrate on the work at hand. If I had another baby, I'd want a midwife again, even though I know odds are she'd only get there at the last minute. DD2's shoulders didn't slide right out like they should have. I'm not trying to be overly dramatic, so let me be very clear that there was no real emergency, we did not have a shoulder dystocia or anything like that, but she was a little sticky and the midwife definitely was a help in maneuvering her out. Again, not something I want to have to worry about.
I know that there aren't as many problems that would require monitoring in really fast labors, so my perspective is different than some people's. For me, there's no reason for anyone to be monitoring - the baby is coming and it's probably coming before anyone has time to notice anything wrong. But I want someone else there to notice if the cord is around the neck and therefore needs to be unlooped or to help me if the baby is a little sticky. Just my opinion and experience.
Edit: Sorry, this didn't seem so related to hospital births, but my point was that I can see why someone might want to have someone else
catch the baby, even if they didn't want to labor
at the hospital.