It's taught in even the most basic teaching curriculum. I learned about it as a teenager learning to teach swimming. To be honest, it's nothing new or special, and I mean, I don't know where you're coming at with the snarky comment about management, but humans are human and sometimes _how you say something_ matters as much as _what you say_. Nobody likes taking criticism, so it helps blunt the blow, while still allowing for critical feedback to be communicated and heard.
It's been taught / used for a long time in North America, I can't speak for other parts of the world. It reminds me of the, "it's not you, it's me", break-up technique, but maybe I just watched too much Seinfeld.
I think it depends on how well it's done. Yeah, if you just transparently sandwich the criticism, it'll come off as a stupid management technique. But if you figure out how to do it genuinely, it can help.
