My thought on this was that something had come up as she was set to deliver, and there was a realization that the woman could not sustain another pregnancy. If so, this is really a terrible thing to face at what should be a time of pure joy.
Something could have come up even before delivery, and waiting a few months after delivery for your fallopian tubes to settle down would make sense. Even when religion is not at issue, surgeons don’t generally like to do this surgery right after childbirth. At least that is how it used to be back in “ancient times.”
I agree that this is a “teachable” moment - what I took away from this was a Catholic hospital was trying to avoid being sued over refusing to allow sterilizations. Gotta be more to the story, but lousy reporting is the rule of the day for whatever reason.