The banality of evil was not presented as a doctrine. Arendt presented the trite affect and emptiness of Eichmann in the context of her analysis of totalitarian organizations. The process of terror is not just the outcome of certain beliefs but has its own physics. Consider this from part three of The Origins of Totalitarianism:
"While under present condition totalitarian domination still shares with other forms of government the need for a guide for the behavior of its citizens in public affairs, it does not need and could not even use a principle of action, strictly speaking, since it will eliminate precisely the capacity of man to act. Under conditions of total terror not even fear can any longer serve as an advisor of how to behave, because terror chooses its victims without reference to individual actions or thoughts, exclusively in accordance with the objective necessity of the natural or historical process. Under totalitarian conditions, fear probably is more widespread than ever before; but fear has lost its practical usefulness when actions guided by it no longer help to avoid the dangers man fears. The same is true for sympathy or support of the regime; for total terror not only select its victims according to objective standards; it chooses its executioners with as complete a disregard as possible for the candidate's conviction and sympathies. The consistent elimination of conviction as a motive for action has become a matter of record since the great purges in Soviet Russia and the satellite countries. The aim of totalitarian education has never been to instill convictions but to destroy the capacity to form any. The introduction of purely objective criteria into the selective system of the SS troops was Himmler's great organizational invention; he selected the candidates from photographs according to purely racial criteria. Nature itself decided, not only who was eliminated, but also who was to be trained as an executioner.
No guiding principle of behavior, taken itself from the realm of human action, such as virtue, honor, fear, is necessary or can be useful to set into motion a body politic which no longer uses terror as a means of intimidation, but whose essence
is terror. In its stead, it has introduced an entirely new principle into public affairs that dispenses with human will to action altogether and appeals to a craving need for some insight into the law of movement according to which the terror functions and upon which, therefore, all private destinies depend.
The inhabitants of a totalitarian country are thrown into and caught in the process of nature or history for the sake of accelerating its movement; as such, they can only be executioners or victims of its inherent law. The process may decide that those who today eliminate races and individuals or the members of dying classes and decadent peoples are tomorrow those who must be sacrificed. What totalitarian rule needs to guide the behavior of its subjects is a preparation to fit each of them equally well for the role of executioner and the role of victim. This two-sided preparation, the substitute for a principle of action, is the ideology."
-Page 165, Harvest Hill edition
From this explanation, we can see the psychology of Eichmann as a result of this process in himself. This is a lot different than saying evil could just come from any "ordinary" person.