Having had two C-sections, and expecting to have a third soon enough, I'd like to throw my two cents in.
The only part of me that was "restrained" during my c-section was the arm my IV was inserted into. After the babies were delivered, they completely sedated me, so I can't speak to what happened then, but I woke up entirely unrestrained.
I've also been present for my daughter's tonsillectomy, and they DID restrain her arms. I was told it was in case she had an adverse reaction to the anesthetic. Which, turned out to be necessary, as she woke up post-op without recognizing anyone--including me, and fought with her entire being to break free.