While the OP's assertion is ridiculous, let's not equate labor pains with the need for surgical anesthesia. Many first-time mothers approach labor with the attitude that the pain involved is always more than an average person can handle and request medical interventions before their labor has even begun.
We should be aware of some of the motivations of those who encourage this mindset. When I worked at a hospital, there was a bit of a controversy because the L&D nurses were encouraging women to wait until they actually experienced pain that they wanted relief for before requesting an epidural rather than out of fear of what was to come. Of course, this resulted in many women discovering that labor pains are in many cases more like a high degree of discomfort rather than an unbearable pain. When the company providing anesthesia services found out about this practice among the nurses, they complained and the nurses were no longer allowed to make any recommendations to the laboring mothers.
I'm generally not in favor of labor interventions mostly because the question of what is causing the huge increases in things like autism and allergies has not been solved. I once was interviewed by a grad student looking to do a study on a possible link between labor interventions and autism -- her study was specifically regarding either Pitocin or epidurals, I don't recall which -- but she was having a very difficult time finding people who had not used the drug in question during labor.
Nonetheless, there are many times when pain alleviation is advisable and there is absolutely no religious reason not to take advantage of this medical aid whenever the need arises.