Naudi Aguilar of Functional Patterns is actually highly critical of the lack of transverse plane training in CrossFit style programming and much of modern strength and conditioning. He argues that real human movement has a large rotational component, and training exclusively in the sagittal plane neglects this movement requirement. However, most of the rotation-specific training you’ll see in typical strength and conditioning doesn’t train rotation, per se, but the ability to nullify rotation. We train to not rotate at the spine when forces would otherwise force rotation.
I think the sweet spot is probably somewhere in the middle. I don’t think we can completely neglect the need for controlled dynamic rotation in human movement. There are just too many disciplines that require it. As David said, much of the rotation we perceive is actually occurring through the lower extremity, but unless the hips and shoulders remain perfectly squared off, spine rotation has occurred. Training for anti-rotation is a start, much like building a plank will help a beginner learn the push-up, but it is incomplete.
I think rotation of the spine is allowable and important, but it has to be recognized that there is a finite physiological limit to the ability of the segments to rotate on one another. This means that an important feature of training the rotational athlete (read: human) is teaching them to recognize and control rotation within safe biomechanical ranges. On top of that skill component, training needs to enhance their ability to manage eccentric forces through the supporting musculature (the coiling part) as well as their ability to quickly change direction once the rotation has been slowed (the uncoiling part).
Now, discs have been mentioned, but the disc is really going to be at risk if rotation is combined with sagittal or frontal plane movements of the spine (flexion, extension, lateral flexion), as this sort of “unwinds” the connective tissue surrounding the disc. If the rotation is pure(ish), then you really only have to worry about the physiological end ranges of the facet joints, which have a varying rotational capacity across the spine. The lumbar spine allows very limitted rotation, while the cervical spine allows the most. The thoracic spine allows enough and, as was mentioned, is where much of the rotation in sporting activities comes from, since we like to keep our eyes on the prize.
Okay, long-winded, but hopefully somewhat enlightening. Don’t demonize rotation, just respect it and train it progressively and properly.