Mankind has bred dogs for various kind of tasks, and, when it comes to researching the various breeds, inevitably you come across some breeds that had no apparent purpose except for companionship. Take the Bichon Frise for example. This is a breed of dog that if owning pets somehow became illegal, the breed would not survive because it is a) small enough to become coyote food, and b) willing to please humans.
I have heard of bichons who were young and healthy when their owners passed away and they would do nothing and eventually died of a broken heart/starvation.
I think that if we did not have pets, we would have a lot MORE animals die on a daily basis than we have now. And, if you spay or neuter early enough, the animal doesn't know what they're missing.
For better or for worse, humans have domesticated animals for several uses, one of them being companionship. It's not like we can reverse thousands of years of history by no longer having pets. If we did that we'd see more animal cruelty, suffering, and death than we would ever imagine.