On the surface, no kill seems to be the right thing to do. Under the surface, we begin to understand that most shelters do not have the cage space to humanely house animals long term, until they are adopted. Many animals cannot hold up to long term confinement.
The best way to see how No Kill can fall apart is to go to: https://www.peta.org/issues/animal-companion-issues/animal-shelters/no-kill-policies-slowly-killing-animals/. PETA has been monitoring the failures of No Kill.
When an animal shelter makes the announcement that they are going No Kill, the first impact it that people considering the surrender of their pet feel they can down give up their pet guilt free. Animal shelters begin to see an increase in intakes. With a new No Kill shelter in the area, people from outside the area will make the drive to the shelter to surrender their pet.
The most effective way to go No Kill is to reduce intakes. With increasing intakes, the shelter will either be forced to throw funds into increasing cage space, or find ways to decline intakes. The City of Austin Texas, had to spend millions of dollars in an effort to try to maintain their No Kill status. Other shelters begin to turn people away due to overcrowding. Most shelters are obligated to take in stray animals, so pet owners report that their own pets are stray so as to surrender them.
The worst part of No Kill is forcing animals to remain in cages for long periods of time. It is tragic that volunteers will put countless hours into trying to maintain the socialization of an animal, only for the animal to become eventually cage crazy and be euthanized.
The pressure to become No Kill is so great, many animal shelters have been accused of doctoring their disposition statuses to give the appearance of a higher live release rate.
The natural evolution of society is sending us down the path to lower intake rates. We are eventually going to become a humane community.