Watch the 2017 Asimov Debate from the American Museum of Natural History. It was a great one. I did not expect the answer to the question of whether we can do this. No spoiler from me. Settle down for a couple of hours with a good drink for this one.
This debate discusses a wide variety of issues, including genetically modified organisms, agriculture, environmentalism, extinction, quality of DNA from preserved extinct animals, morality, animal welfare, legal issues, etc.
For a sample, just consider the question, if we brought back a mammoth (or mammophant) from extinction, is it automatically an endangered species? What is its “natural range”? What are its natural habitat and food? Is it moral to bring back a species adapted to the arctic in an age of climate change?
P.S. Neil is a bit out of his element on this first Asimov Debate that is NOT related to cosmology, astronomy, or astrophysics in any way. But, as he points out Isaac Asimov wrote about a variety of sciences, some of which did not even really exist at the time he wrote about them, such as robotics. So, de-extinction is perfectly within lines to honor the late Isaac Asimov who spent many hours at the American Museum of Natural History in New York.