So i have some perhaps-completely-inaccurate theories about this. This comment contains minor spoilers for part 3; avert your eyes, folks.
I think that by that point in labor, your pain receptors were basically firing on all cylinders. My understanding about pain is not very sophisticated, but a lot of things affect how it's perceived. Basically, because you'd been having contractions for so long, you were feeling pretty much every sensation as horrible pain by that point. This was probably related to why you found the IV so painful, as well as to the back and leg stuff. You were also extremely touch-sensitive at that point (probably related too), like when the nurses needed to move the monitor and stuff.
It seems to me the risk was that, if you'd endured that for several more hours unmedicated, followed by over two hours of being manhandled by four people who were supporting you while you pushed, you might well have been miserable enough not to be able to appreciate the actual birth of your child. That would have been worth enduring in some circumstances (such as medical risk for one of the participants, as you note), but, insofar as it was one of the most fucking incredible things i have ever seen, i'm inclined to think that not being able to be mentally present for it due to pain would have been a big loss.
I will finish by disclaiming again that i may be totally wrong about any or all of this.
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I think that by that point in labor, your pain receptors were basically firing on all cylinders. My understanding about pain is not very sophisticated, but a lot of things affect how it's perceived. Basically, because you'd been having contractions for so long, you were feeling pretty much every sensation as horrible pain by that point. This was probably related to why you found the IV so painful, as well as to the back and leg stuff. You were also extremely touch-sensitive at that point (probably related too), like when the nurses needed to move the monitor and stuff.
It seems to me the risk was that, if you'd endured that for several more hours unmedicated, followed by over two hours of being manhandled by four people who were supporting you while you pushed, you might well have been miserable enough not to be able to appreciate the actual birth of your child. That would have been worth enduring in some circumstances (such as medical risk for one of the participants, as you note), but, insofar as it was one of the most fucking incredible things i have ever seen, i'm inclined to think that not being able to be mentally present for it due to pain would have been a big loss.
I will finish by disclaiming again that i may be totally wrong about any or all of this.