I _did_ work at an open-intake shelter, aka 'kill' shelter. We were the shelter that animal control brought all the animals they found in the county, we were one of the only local shelters who would accept any pet people wanted to abandon, we were responsible for housing all of the animals being held in court cases (fighting rings, dogs found during drug raids, hoarders, etc).
We tried so, so hard to get every pet out alive that we could.
But there'd be days, very frequent days during the summer, where we'd literally take in more pets during a day than we had cages in the entire shelter. Some pets would leave every day, of course - adoptions, some taken by rescue groups, some taken by 'no-kill' shelters looking to fill their spots with cute, adoptable pets.
But then there were the rest.
The ones that were too old, too shy, to sick, too angry. The ones that for one reason or other never caught anyone's eye. Then what do you do? There's one kennel, and two pets. One just got there. The other has been there for weeks. Both are super sweet, super cute - there's nothing wrong with either, they just don't have a home.
A lot of shelter staff ended up with multiple pets because of this. But even then. There were so many pets.
So please don't disparage kill shelters. If you don't want that situation to happen, help, damnit. Help with TNR programs. Spay and neuter your pets. Don't buy from backyard breeders. Donate to your local shelter (the one I worked for way back finally got enough funding to build a new, bigger facility - doesn't solve the problem for sure, but it took some of the heat off). Even doing things like volunteering to socialize the pets in the shelter can help those pets keep enough of their sparkle that they'll get adopted. Stop bitching about the problem and get in there.