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. This is a poor excuse for giving up a dog. A dog can certainly be house trained. First, consider crate training. There are numerous books and articles on the subject.