I'm not sure I'd consider it inhumane most of the time...in some cases when a dog is really going downhill in a shelter situation, depressed, etc, then it's questionable....but I know quite a few dogs in shelters for years that are seemingly happy and healthy, enjoy their walks and socialization, eat, in good health, respond happily to volunteers, etc.
My concern is the resources it takes. If a dog is really unlikely to be adopted, because, say, they have a chronic health problem or are a resource guarder that can only go to a trainer home...how many very adoptable dogs are being PTS in ACC because this dog with seizures who hates other animals is taking up a kennel in our local private no-kill for 5 years?
It's a hard decision and I don't know the answers and it's often case by case and really when it comes down to it I think most dogs are worth saving/rehabbing to SOMEONE, so it's hard to say. A lot of times I see dogs in our private shelters, many with health issues, and think the resources (time, money, space, volunteers) are ridiculous TBH. They could have saved ten or fifteen other dogs sometimes with what they put into one heartbreaking story. But does that mean the dog that was crushed by a truck and then dumped at the shelter door with 23 broken bones doesn't deserve a chance? I really don't know. I guess it brings publicity and donations to the rescue, to have dogs like that who make local news and papers. Sometimes I see the vet bills and shake my head at the fact they could fix and vaccinate the whole rescue capacity with what they spend on one dog's surgery.