In theory it would be good if all shelters had a no-kill policy.
In practise it just creates another problem further down the line. A shelter can only take so many animals before it runs out of space to house them, or runs out of money to feed them and pay vet bills. If a shelter has a guaranteed no-kill policy then sooner or later it will have to turn away animals. If people are trying to surrender an animal and no shelter nearby will take it, sooner or later they will either kill it themselves or turn it loose. If they turn it loose and it hasn't been neutered/spayed then it starts to contribute to the problem of stray animals.
It seems to me that a better solution would be to reduce the numbers of animals left to shelters in the first place. If resources are going to be thrown at constantly enlarging animal shelters to make sure that no animal is ever put to sleep, perhaps those resources might be better used to make it easier/more affordable to get pets neutered to prevent unwanted animals being born at all.
A book I have about cats (I recently adopted a kitten) claimed that every year something like 3 million cats are euthanized in the United States alone. That's a huge number of cats to house in animal shelters for however long they live, and even assuming as many as half of those cats were put to sleep due to illness or infirmity that still leaves a huge number of unwanted cats. And that's just cats, since so many breeds of dog can grow so much bigger than the biggest cats the problems are even more serious where dogs are concerned.