Just because they can, doesn't mean they all do, or will.
Of all the birds I have owned or fostered, I have had two that were what I call "cognitive." They all have some ability, whether or not they choose to interact with you. But, nothing is guaranteed.
Alex was picked at random from a pet store. That was the point of the experiment. Totally at random. Nothing special about that bird. Then she worked with him 12 hours per day, six days per week.
Not only could he talk, he could add, subtract, multiply, and could verbalize the differences between colors, shapes, textures, etc.
When I got my CAG, I went to a seminar taught by Dr. Pepperburg, where she explained some of the concepts and training methods. Fascinating stuff for bird nerds...
MY FAVORITE ALEX STORY:
Dr. Pepperburg was doing a research fund raiser, and was demonstrating what Alex could do. She gave him a spelling test, and was giving him a grape as a reward.
So, she gave him a word. He spelled it correctly. She gave him a grape. He spit out the grape, and told her "I want a nut." She was out of nuts, and told him he would get his nuts later...
Then she gave him another spelling word. He spelled that one correctly. She gave him another grape. He again spit it out and said "I want a nut."
She again told him she didn't have any nuts and gave him another word to spell.
After the third time spelling a word correctly and not getting his nut, he looked her in the eye and said: "I want a nut. N-U-T! NUT! He actually sarcastically spelled it out for her... then he refused to do anything else until someone went and got him his nuts...
THAT is not a mimic. THAT is cognitive.
My CAG is cognitive. If you are looking for the bird with the most superior cognitive abilities, CAGS are probably first on the list. But you get what you put into it. They don't come like this. This stuff has to be taught.