In your opinion then, the government may not outlaw polygamy, polyandry, consensual incest, necrophilia, beastiality? Killing animals in the privacy of your home OK (no people are harmed)? Can the government regulate contracts? Adjudicate disputes between parents and children? Blood Relatives? Confiscate personal property with just compensation?
Your concept of government is juvenile. The decision of what areas of personal life the government should regulate is THE most important reason for having State Assemblies and Congress.
No, the government may not properly outlaw any of the practices you describe, as long as they involve only consenting adults. IMO, animal cruelty is a legitimate area for government regulation, since obviously the animals can't consent. Some forms of bestiality would fall under the cruelty umbrella, but if someone enjoys encouraging their horny canine to hump them in their own home, I hardly see any benefit to government agents undertaking a prosecution. As far as I know, there's not a single state which outlaws humane killing of animals in one's own home, whether for food, or euthanasia of sick/unwanted pets or farm animals, or pest control -- nor should their be.