They normally don't go into details, nor is there an "anti-human" thing going, but it makes the premise of evolution of existing species more interesting and workable. Oddly, "The Future is Wild" assumed humans just left the Earth for some reason, and were observing the life from distant worlds. Maybe the Earth got cooties or something.

In reality, humans are unlikely to go extinct under any circumstances that would not kill off the rest of life of Earth, and if they somehow did, most future mammals and birds would probably be, as SDF alludes, descendants of dogs, cats, cows and chickens.