I think the current prevalence of c sections renders the very suggestion of the other procedure rather terrifying to the parents.

No it is not routine to do that any mire

Copied from Mayo Clinic:
Routine episiotomies are no longer recommended. Still, the procedure is sometimes needed. Your health care provider might recommend an episiotomy if your baby needs to be quickly delivered because:

Your baby’s shoulder is stuck behind your pelvic bone (shoulder dystocia)
Your baby has an abnormal heart rate pattern during your delivery
You need an operative vaginal delivery (using forceps or vacuum)

I opted for no episiotomies. This was in the 80s when it was still standard. They billed my insurance for one, though, along with an epidural which I didn’t have either. And stitches, which I didn’t have.

Routine episiotomies aren’t standard anymore. Though they’re still used for certain situations like @jca2 mentioned.

My ObGyn said that natural tears actually heal better than a clean cut.

According to the Mayo Clinic episiotomies are rarely use but still an option IF the baby is in distress & time becomes critical.

About 28 years ago after I couldn’t get my big headed son out I remember the nurse telling me that “we had to cut you from stem to stern!” I don’t know how they did it without getting into my rectum area. That was something I didn’t need to hear!

LOL