One of my next builds will have Chinese carbon bars and an integrated stem, although I didn't weigh it before starting assembly.

I think it is a good point that the aluminum bars are already pretty light.

The carbon bars often have features that the aluminum bars don't have such as internal cable routing tubes, and more ergonomic shapes... all of which would add to weight. I wouldn't be surprised if some of the Chinese integrated stems are aluminum stems with a carbon wrap.