I imagine in the regions of Turkey where the Anatolians are used the predator population has long ago been reduced through hunting and trapping. In such an environment a pack of Anatolians guarding the herd would work just fine.
The content of your imaginings relates to why Anatolian shepherds are still poor. The reasons are simple: Large dogs take a lot of food. The food is meat. Meat is what they are selling. Dogs aren't perfect. They take a lot of time to train. It's a big investment and some don't make it. Those are losses too. Meanwhile, the soil needs the blood, guts, and bones the dogs are eating. The soil makes the raw material for his sheep. It's a losing game.