Oh sure, it sounds like a good idea. But think of all the things we've lost to natural selection:
Haast's eagle: EXTINCT
According to Notornis, a peer-reviewed journal for the study of birds, Haast's eagle is "the largest eagle known to have existed." Ate a diet consisting of moas, which were twelve-foot tall flightless birds. Its bones were first discovered by German geologist Julius von Haast, who, lacking a German equivalent of the English phrase "hella ginormous", named the bird after himself instead. Between its size, and its natural habitat of New Zealand, Haast's eagle was the real-life version of Gandalf's Eagles in Return of the King.
Every Dinosaur That Ever Lived: EXTINCT
I know, I know, "they evolved into the birds of today". Do the birds of today make me feel like Sam Neill in Jurassic Park? No, they do not.