Most of the people morally outraged that we eat meat are outraged that we kill the animals to do it, or the conditions that they are raised in. They wouldn't be angered if we only ate wild animals that died of natural causes. Of course, realistically that wouldn't be safe. We wouldn't know what the animal died of, or how long it had been dead, which would make it likely that it had pathogens from cause of death or rotting.