To me, it makes no sense to slaughter millions of dogs in dog pounds and then just throw their bodies away. Why not sell the dead dogs to people who want dog meat, and then use the profits to build bigger shelters that can keep the dogs alive for longer? It's better for the dogs and it's better for the people who like to eat dogs.
People can't eat animals that were killed with drugs, and usually don't want to eat animals that died from disease. There's a USDA inspection process, you can't just sell meat out of the back of a shelter.
Those animals are sometimes cremated, but are often picked up and sent to rendering plants where they are used to make products and additives that are safe to make from such animals, such as bone meal and the like, that gets added back into animal feed, and other non-food products.
Euthanized and dead horses can also be picked up by rendering plants, they are here, and I have no problem with that, as an alternative to hiring a backhoe. When a 1200 pound horse dies, there just often isn't a dignified way to handle it.