How, in Animal Farm, does Napoleon's use of of obedience tactics help the farm?

In a general sense, Napoleon's tactics lead to greater productivity on the farm. His insistence that the animals follow instructions and remain loyal guarantees that the animals remain committed and unquestioning. In such a system, more focused and productive labor ensures greater returns and bigger profits. Furthermore, the tactic guarantees a servile attitude and minimizes the risk of recalcitrance and rebellion.
Napoleon ensures that the animals remain obedient not only through propaganda, misinformation, and deceit, but also brutally enforces control by slaughtering those who dare rebel against him. The best example of this occurs in chapter seven, when the three hens who resisted his instruction to sacrifice their eggs are executed by his dogs. Animals who supposedly plotted against him also suffer the same fate. In this manner, Napoleon establishes a merciless tyranny. He becomes supreme leader and his authority cannot not be questioned.
The success of this strategy is proven by the successful completion of the windmill after it had been destroyed, the lack of wastage on the farm, and the general air of commitment, although enforced, that exists. This is best encapsulated by Boxer's two maxims: "I will work harder" and "Napoleon is always right." These statements reflect the overall sentiment on the farm, with the exclusion, to a certain extent, of Benjamin. Although he is quite cynical and recalcitrant, Benjamin does what is asked of him.
Although Napoleon's strategy leads to the successful running of the farm, it is, sadly and ironically, only the pigs and Napoleon's dogs who truly benefit. They live lives of luxury whilst the other animals are always tired, hungry, cold, and miserable.
The greatest irony lies in the fact that the gullible general animal populace believe they have achieved utopia when, in fact, their dream has resulted in a dystopian reality that is worse than the one they experienced under Jones's rule.