I first noticed Focus breathing on a pair of cheap 70-200mm lenses, this link confirmed it. Also covers the white issue, and a few other bits.
https://www.youtube.com/watch?v=P80BpSQIIto
You can just put a white or camouflage cover on the black lens, although no other manufacturer seems bothered about the issue. I would have thought keeping the camera temperature down would be more important yet their cameras are all black. And why have a white lens with black rubber? It would be fairly easy to make white rubber instead and the price isn't the concern here.
I've noticed the effect before quite a bit when doing extreme macro work and focus stacking, just never heard the effect called focus breathing before. At first I didn't quite get why it was called that, but the more I think about it the more it fits.
As to no other manufacturers using them, I was sure I'd seen other white lenses, Sony make white telephoto lenses, and nikon used to. I don't know about other brands though.
I still maintain it'd be interesting to do some kind of experiment to see just how much effect, if any, the colour of the lens barrel has on IQ.