This is the most ridiculous idea that ever has been - people will dump
their animals, people will state they are strays and that means the
animals are in the shelter longer before they can be adopted - whoever
thought of this idea should be fired!
Hiding from the problem won't make it go away. This is like the police department just refusing to take crime reports. It doesn't make crime go away. Incidentally LAPD did do this to try to make it seem like crime was down. They got caught and now they must take all reports.
Any owner who dumps their animal at a kill shelter can not be trusted to do right by that animal when turned away. They will set it loose. It'll get ill, injured, pregnant, maybe killed. Or else the owners may just murder their pets by drowning kittens, throwing puppies out the window of moving cars.
I think this is a bad idea. It is putting the problem of pet overpopulation into the hands of the irresponsible owners. They can't just shutter the shelters doors and proclaim themselves "No-Kill!" Boks can't just refuse to do his job in order to better his numbers. The numbers represent animals lives. They aren't just an arbitrary measure to try to make Boks look good.