Jercarp

I use plaster washers all the time for this very thing. They're cheap and come in bags of 100. I keep them in my truck so they'll always be on hand.
I do appreciate the video however because you do preface it with "in a pinch", even though it's not a better way. I carry pipe strapping as well.

I agree with Axlp, it would have been nice to see the "other side" of the world of building & contracting. However, they only had a half hour each week to schedule in all the many things that were going on, and the show was produced to be more of a "can do" presentation. It was also geared toward the general populous of homeowners, showing them ideas and possibilities, and not towards the much smaller world of the general contractor or tradesman and their own particular needs and problems. Don't get me wrong...I, as a carpenter-contractor, was able to glean from the show many hours of new ideas & techniques over the years.
The last point is, (and I'm fairly certain I'm not wrong here), Norm had little to do with the content, direction, and flow of the show, and what ended up on the cutting room floor. That's ultimately the editor's and director's job. I'm sure he had input because of his vast celebrity and skill, but the decision to not show screw-ups and keep the show on a "here's what we choose to do and how it's done" level was not his.

I stopped watching the show some years back because it so paralleled my own life, and after 30 years of working on houses old and new, I would rather read a book or go for a good walk.

Been doing this technique for years and years, we call it a "blow patch". It's good to bring up once in a while so others can pass it on.
The reason I posted comment?...You guessed it. You need to mud the four sides of the sheet rock patch so the compound squeezes in to seal and glue the joint between the cut wall and the patch. Otherwise the only strength around the patch is the thin paper and what little compound was applied.
I see some posters beat me to the point, but it's an important one. The patch will give way otherwise, I've seen it happen from this very mistake.

I don't recommend this technique be used for patches much bigger than what you show, even though I have done it in the past. Bigger holes should be backed up with wood or metal cleats inside the wall covering both edges of the seams.