There is NOTHING wrong with having these people. There is something wrong with using them to save animals before all the people are rescued.
Besides, your argument about equipment is hollow. If you can rescue an uncooperative dog or horse, you can rescue a person that cooperates.
The article is talking mainly about rescuers plucking dogs, cats, puppies and kittens from the water. Most of these animals are small and light.
And if you drop them, they don't sue.
As for horses, I didn't see any detail about that, but I doubt there are a lot of horses left in the city of N.O. If there are many carriage horses left behind in the historic district, I would be surprised. But better to save them than have their rotting corpses adding to the mess. And NO, you cannot rescue a human in the same way as you can a horse.