What's the normal procedure then for adding a cable to an existing
electrical panel? Surely there's a way to protect and secure the
incoming cable other than tearing into the wall just to tighten a nut
on the backside?

The nut goes on the inside of the box. Put the clamp part onto the
cable before snaking it through the wall. When you pull the cable
into the box, the male threaded part of the clamp pulls right into the
hole. Install the nut and tighten.

Hmm.. Interesting idea. It would mean drilling a larger hole in the wall
plate that the clamp can fit through, but otherwise it sounds like a
workable solution.

Thanks!

Anthony