They don't have full-time staffs. They don't get paid to do this. Just remember that you may have to keep your dog until an adoptive family is found. That's what obedience classes are for. There is no such thing as a dog that cannot be trained to be a well-behaved member of the household.
Most canines thrive when given basic obedience training.
Please give your dog the benefit of the doubt and take them through a basic obedience class before you give up on them. A dog can certainly be house trained. First, consider crate training . There are numerous books and articles on the subject. Then consider the dog.