The should question is already overtaken by events. We will use gene drive technology and are doing so already. The question becomes to what extent and with what safeguards.
Humanity pushed evolution into overdrive at least 500 years ago, when the “age of discovery” and the “Columbian exchange” mixed species that would never have met absent humanity. Our drastic changes in land use and now global climate change produced novel environments that favored some species and doomed others. We are like the man in the middle of a frozen lake who notices the ice is cracking. Maybe the best advice would have been to stay off the ice, but that no longer makes a difference. There are only choices going forward.
Gene drive may be used to alleviate suffering by eliminating some diseases. It may also be used defensively to help plants and animals adapt to climate and environmental conditions coming too fast for ordinary evolution to cope. We will not fail to use this new technology. Let’s try to do it wisely.