The other two abbots at Leibowitz Abbey are the protagonists of their sections of A Canticle. But Arkos is not. And for good reason—the guy's a Grade-A Jerk.
When we first meet him, Father Cheroki describes Arkos as a "were-bear only incompletely changed into a man" (4.2). Later, Francis calls him "the perpetual inquisitor of his soul" (9.25). Both are fitting descriptions.
Allow us to explain.
He bullies everyone at the abbey with the power of his office. He prevents Francis from taking his vows for seven years straight (7.1), and even beats the novice with a hickory ruler simply because the boy won't tell a lie (4.71-4.74). One can only imagine what he'd do to poor George for cutting down that cherry tree.
We imagine something involving thumb screws.
But the question is: why is Arkos such a meanie? The answer is simply: politics. Abbot Arkos wants to see Leibowitz made a saint by New Rome, and he thinks nothing "could damage the case worse than a whole flood of improbable 'miracles'" (4.11).
To prevent this flood, he abuses Francis so that Francis stays silent. He even closes the shelter after the documents and relics (the Memorabilia) "[are] quietly rounded up" (6.22).
But hiding knowledge from the world seems very anti-Leibowitz, and contrary to the goals of the Memorabilia project. So Arkos is almost as bad as characters like Hannegan and the Defense Minister. You don't see Dom Paulo hiding anything from Thon Taddeo, right?
Sure, Hannegan and the Defense Minister killed people by manipulating politics and information, and Arkos only doled out a few epic spankings. And maybe a bit of psychological scarring to poor Francis. But even if the scale of their evil doesn't totally match up, Arkos shares a lot of qualities with the other antagonists of the novel.