I would point out that just because not many coaches approve of a style does not imply that not many dancers dance it. I also think that Chris characterized it as the "Luca" style, not the "Luca and Lorraine" style.
As far as the spine/back arch, if you look at any anatomy book (as my coach has us do often), you will see that the human spine has a natural arch to it. The top of the spine and the bottom of the spine curves while the middle is straight. That is all you see when you see someone like Luca dance because his dancing is *natural*, comes from what the body does naturally and, thanks to years of evolution, quite efficiently and easily. People who teach the various iterations of "scooping your hips", "tucking your hips", "straightening your spine", etc. are taking away the naturalness of human movement.
I have to somewhat agree with Josh that while it should be "natural," for many of us, it's no longer natural because of all the unnatural things we do to our bodies.
I've recovered twice from serious back injuries, and countless times from more minor ones. (I'm in one of the top back injury professions.) My last major recovery involved a lot of physical therapy restoring the curve of my spine. (And straightening out all of the compensating I'd been doing from years of disc herniation compressing spinal nerves.) But it was just remarkable to me how unlike the skeleton that hangs in anatomy classes my skeleton had become.
I wouldn't necessarily say that all of the "scooping your hips" and "tucking your hips" and "straightening your spine" is actually taking away from natural movement though. Sometimes we have to do bizarre things to get back to what is natural movement.
Getting my back, that's been altered by my various injuries, to do something in a more "natural" manner is going to take different directions for scooping and tucking and straightening things than getting any other person's back, with it's lifetime's alterations, to move in a more natural manner.
Natural is rarely reality. And turning reality to natural is an individual process. A "natural" arch for some is a very unnatural arch for others.