I don't think the dentistry analogy is a great one, because lots of women do prefer to give birth without pain relief, or with maybe just gas and air rather than full anaesthesia. Certainly a far higher proportion than that of patients refusing pain relief for other procedures. So I believe there is an intrinsic difference between birth, and other medical procedures.
That belief doesn't carry an intrinsic value judgement though. It's up to women to choose how they want to give birth (assuming no other specific medical needs which make intervention unavoidable)
I chose to have my babies with just gas and air first and foremost because I was keen to deliver in a midwife led unit rather than hospital, and I was not keen to have an epidural anyway because there does seem to be a higher chance of then needing further intervention. That was my choice, it doesn't make it better or worse than anyone else's. I personally found it very empowering, but again, other women might find having a hospital birth with full pain relief empowering.
I just don't like the analogy people make that 'you wouldn't have a tooth pulled without pain relief' because I think it belittles the fact that a high percentage of women do actually approach child birth in a different way to other procedures. Many women would accept an injection for having a tooth out, or pain relief for minor surgery etc but opt to try to give birth as naturally as possible. So, they have reasons, which matter a lot to them even if not to others