> Would storing genomes be enough, similar to backing up data until it is needed?
I don't think so, because many of the endangered animals are representative of entire ecosystems. Consider orang-utans and the forests they inhabit (many of which are being destroyed to collect palm-oil). If the animals have gone, it is even harder to make people want to preserve their environments in the face of relentless commercial pressure. Some endangered animals also help shape the ecosystems, e.g. when they are apex predators.
Once the animals are gone, recreating their communities is significantly harder. As stated elsewhere, most animals are better raised by their own species rather than humans outside the cage. For primates (e.g. woolly monkeys) individuals that have been raised in isolation in captivity also don't make good parents when they do eventually breed, sometimes abandoning viable young.