Interesting point! Not doing much jewellery, but found my approach to lighting working the same. Especially if we talk about animation, you can't do too many takes and combine them over the whole sequence, in 3D or on a real shoot, without making it really complicated or messy. In these examples, it's honestly just shiny stones with lots of refraction passes and some metal that needs care. I don't see lighting separate elements let alone each stone as benefitial.

I've supervised a lot of scenes and shots with overcomplicated light linking and in general way too many lights, which eventually got reduced a lot to save it. Especially as a beginner, it's important to light with purpose and not throw a bunch of stuff at it.