I don't know about the "track record" you speak of. I suppose we would have to develop some time lines and investigate it, with regards to the wolf population. We have certainly evolved and gotten smarter over the decades about managing wildlife. But there are some things to consider with regards to preservation of certain species.
The predatory wildlife in the USA is certainly making an aggressive come back. If the wolf population were to thrive in the south, they could certainly help with the destructive feral hogs and such. But they would also, or maybe more likely, kill the easier prey that is penned up, slower and more nutritious for them. They would likely also kill cattle. It wouldn't be long before there would be a cry to "cull the wolf packs" and the cycle would start again.
As others have said, many places have an overpopulation of deer. In most of the USA, deer do not have natural predators. When they overpopulate, they starve, get sick and spread disease through the herds. With natural predators, the weak and diseased would get eaten. The only problem is, predators are lazy creatures too. They eat the easiest meal to catch. If two or three wolves are considering a deer or a cow for dinner, it might not take them long to figure out that the domesticated cow is like room service compared to chasing down a deer.
It's a complicated balance, IMO. The real nature lovers work hard at finding the right balance. The do good planet loving human hating liberals make a career out of complaining and crying about hatred and evil without regards to reality or consequences.
This would apply to Africa too. Face it we are hypocrites. Predators for thee but for me.
Cows come in herds. A herd of cattle is a dangerous entity to a wolf. Even domestic cows will kill a wolf.