I suspect that hunting, field dressing, and butchering lost their mainstream appeal soon after industrialization.
It's one thing to do these things once a month on a hunting trip for leisure versus doing it nearly every week in order to maintain your property or community. It's like the difference between gardening as a hobby versus farming as a lifestyle.
The amount of hunting needed to control the deer population and the population of able bodied and sufficiently interested hunters simply doesn't scale properly in most communities.
Predators who hunt as their main purpose and niche in life seems like a more viable solution if we determine how to keep the livestock predation to an acceptable level.