In concept, what's not to love about them?
In practice, I do know of a cat sanctuary that turned into a de facto hoarder situation despite the people's best intentions, because they weren't willing to turn endangered cats away, but they weren't adopting out as quickly as cats were coming in.
The people running the show really need to decide ahead of time what's capacity, and when capacity is reached, follow a strict one in, one out policy for newly admitted animals. That sounds really simple in theory but it's a lot harder when someone in a crisis situation is sobbing about how you're their beloved pet's last chance. I used to volunteer at a horse rescue and they'd get calls or even visits like that on a weekly basis, trying to get them to take animals that were beyond their remit...I imagine with the greater number of dog/cat owners, it's even more common for dog/cat rescues.
Yeah the in practice element is my lingering worry too. There's always education and due diligence to lessen the occurrences of those crisis situations. Early intervention if absolutely necessary can also be used to make sure those types of downward spirals don't happen as often.
I know cats are seriously overpopulated all around the USA (and world for that matter), so an all around cat sanctuary is very hard to pull of properly. I don't know if the different cat types are different enough to warrant people to create special sanctuaries for each type.
Compared to cats or equines, I think it's relatively easy to make sanctuaries for each type of dog, either by breed, age, health status, etc. In theory, sanctuaries that specialize in each type of dog (however one categorizes) would exist, and whatever category a dog falls into, they would go to that place. If one isn't properly equipped, people can be directed to one that is. Of course, it's possible to be rejected by all of them. In practice, the former already kind of happens? There's breed specific rescues/ sanctuaries, senior dog rescues/sanctuaries that also offer canine hospice, and disabled dog rescues/sanctuaries that pull dogs from kill shelters. Dogs are constantly moving to different parts of the system.
Kill shelters being open to work with rescues is a start. Kill shelters having larger rescue networks is definitely already happening. So the groundwork is there? It's just ramping that up.