How are pigs, rabbits, goats and venison more sustainable? Unless you mean eating meat twice a year.
I live in a farmer family; our cattle needs around one hectare each, because we don't feed them processed food, only grass; because concentrated food is even less sustainable, and more importantly, more expensive than letting them roam (fenced areas)
Rabbit is not sustainable. There were some people trying to commercially rise and sell them and it didn't work. They would need concentrated food, which is expensive.
Goat meat is much more expensive than cows because they are less efficient than cows and pigs and chicken. I know two people who rise goats to sell them, and it doesn't make them money; really, they do it because they kind of like the critters as a pet project.
Only pigs and chickens are more sustainable, precisely because of theirinhumane(?) short life and their genetics. They are very efficient meat producers.
I know poor people who rise chickens and pigs; those animals take longer to reach "maturity", and the meat is not tender; but since the animals are eating whatever they scavenge, it can't be done at scale; again, we would eat meat like twice a year (This might be an exageration, but chicken pig and cow farms really produce all the meat we eat; of those only cows eat grass under the sun)