I have removed 2 medicine cabinets and was patching the hole on the second one when my contractor told me I was doing it wrong. Because thee was nothing to nail to I got some clips that hold the patch in place, put joint compound, taped and then did the compound over that. Several coats, sanding between each and then added texture. The first one I did looked good but he told me I should do a butterfly patch and explained how to do it. I thought my first repair looked great. I cannot tell where the patch is except for the lack of paint. Was I doing it wrong or is this just personal preference?
I will just say that a medicine cabinet size hole represents a fairly good size piece of sheetrock and I personally would block behind it to have something to screw to.
Many ways to skin a cat. So long as you cut it nice and snug, a butterfly patch comes in handy at times and can be nice because you don't have to have tape on hand, etc. Those clips you used are fine to so long as the hole is not to big.