The problem is a technical/legal one. FOr a civil suit, one must have a cause of action. If a person tortures an animal, who has a harm that can lead to a course of action? The only thing harmed is the animal. So technically, the animal is the one who needs to have standing.
Any law would of course provide a human “standing to sue” on behalf of the animal. Otherwise the person would have to argue and show that the person was harmed by knowing about the animal cruelty.
I think it is a bad idea, because civil suits should be for collecting actual damages, not for punishment. If people are being cruel to animals because the current punishments aren’t severe enough, change the law to make punishment more severe.
What animal-rights groups want is civil punishment, so they can act like a police force/prosecuters and go after all sorts of cases they believe are “cruelty” that the actual police and prosecuters would reject.
You’re absolutely right1 Who would have thought thousands of people in California would be out of work over the Delta Smelt!