Well, as far as being "better off", since the dogs that aren't adopted are commonly euthanized, I would think that's a pretty low bar.
It is sad but Oh my gosh if you still want to keep twisting my words apart ,yes IMO putting dogs to sleep is the best thing to do at times. . We had a sweet dog that had cancer and then sever mobility issues and suffering daily. We did everything we could. My daughter held her to comfort while they put the dog do sleep. Same in SXM , dogs get sick and do not find a new home and sometimes its the best option.