Since we're officially off topic and now discussing no-kill shelters, I'm chiming in, again.
If an animal is not adoptable, and a rescue does not have the resources to put the work into them, then I REALLY think the most humane option is euthanasia. It is NOT FAIR to keep animals caged up in an environment that does not meet the most basic of mental and physical stimulation needs. It's cruel. It's wrong. I can not think of a more miserable life for an animal, than sitting in a cage, with minimal interaction, scared and alone. I, personally, would rather be dead.
My ONLY experience with a no-kill shelter was when I got Ellie. None of them were caged. There were multiple rooms with a bunch of cat towers so they could climb and scratch to their heart's desire. It was clean as a place can be with so many cats. Sounds great, right? As we were sanitizing our hands, getting ready to go find our cat, we listened to a small set of rules. They warned us that if a cat is hiding, not to try to coax them out, they're probably aggressive. They said if we see two start to fight, some find someone. Seemed reasonable.
As we were walking through these rooms of cats, I was saddened beyond words. The volunteer changing litterboxes commented on several of the aggressive animals that had been there for years. Can you imagine that? Years of your life spent huddled in a corner. Years of your life spend aggressively defending yourself. Years of your life without a home. I'm sorry... but that's the epitome of cruel.
In my mind HA dogs should NOT be adopted out unless someone has really really proven themselves capable of handling such a dog. How they would do this, I'm not sure. If I had a really HA dog in my care- they would not be adopted out. Sorry.
I get it. Without some rescues these dogs would be dead. I get it. The time limits are too short. I get it. Funds are limited. But.. I really think that euthanasia is a reality of the careless breeding of animals, and irresponsible pet ownership. Until those issues are addressed and resolved, there will ALWYS be animals needing saving, some of which won't be suitable in a family home. In that case, I think that setting them free of their body, or their situation, of their life... is undoubtedly the most humane thing we can do. Keeping them kenneled for years is not justifiable.