I'm suprised nobody has mentioned the possibility of a epidural being ineffective, or the pain of having to wait for anestheisa while in the hospital.
If a woman is choosing epidural meds as her pain relief at the hospital, it can be quite an unpleasant and painful reality when the epidural isn't placed properly, or if the infusion of meds isn't numbing effectively. Then a woman is trapped in bed, tied down with the mandatory BP cuff, IV infusion, belly belts, and probable urinary catheter. How's she supposed to "change position" or use other pain coping techniques now? Can she still get narcotics via IV? Also, it is shocking how often it takes an annoyingly long time to summon the anesthesiologist to administer relief.
So instead of a woman's own abilities to cope with pain (be that hypobirth or her doula or changing positions or breathing or whatever) she surrenders all power to the hospital staff, who may not be able to deliver
(forgive the pun.)
Furthermore, epidural anesthesia often leads to the classic Cascade of Interventions already discussed in this thread, and Pitocin labor augmentation comes to mind, as a fave tool used by OBs/CNMs to kickstart a boggy epidural-slowed labor.
Pit contractions are more intense, painful, and longer-lasting than natural conractions--ask any L&D nurse, and s/he'll probably tell you what my L&D nurse told me when I was induced w/ #1: look at the tracing on the graph paper coming out of the monitor at bedside, and you'll see natural contractions are recorded with a gentle hill-like tracing, whereas a Pit contraction will be traced with a steeper slope, and a slower decay.
As I contemplated my second birth, when I decided on homebirth, I knew I could handle the pain of natural birth because I already endured the pain of a lame first epidural, a second mediocre epidural, and the shocking unpleasantness of Pit contractions all day long.
Not trying to be snarky, but perhaps the OP is intentional with the title: Non-medicated delivery by choice-why?
I guess if I had to be delivered at a hospital with all the trimmings, and be robbed of my birth, I might want to score some meds to dull the experience and make it tolerable. I think there is a big difference between a hospital delivery, an empowered hospital birth, and a home birth.