People have breed different colors into animals forever. You hardly ever see any domestic mice or rats that are brown anymore. I haven't seen a normal Golden hamster in a pet store in a long time either.
Most of our domestic dog breeds are a long way from looking or acting like a wolf even though technically they have the same DNA. And I think most people are glad for that
As for birds, I think they are all pretty the way they are. And yes, my understanding is that most species can't cross breed. I was talking with a breeder a few weeks ago about possibly obtaining a new Blue Crown conure. She had a male and a female and told me I should take the female since my Nanday is female. She further commented "unless you want to breed hybrid conures." To my knowledge though Nandays and BCs can't cross

I do know Nandays can cross with Suns and Jendays though.