...you have to lose genetic diversity to get new breeds...
Have you actually thought about what the word "new" implies with respect to the word "diversity"? Is this kind of the same as Toyota having fewer models to sell when they introduce a new one? No, wait, that wouldn't work unless they quit making some number of the existing models when they introduced a new one.
When a new breed of animals is selected for, do they kill all the previous ones? Isn't this just a variation of "why are there still monkeys"?