I’ll admit I erred in saying he’s of the “highest” moral character but Hank has always been shown to be lawful. His obsession at some points in the show cause him to teeter close to falling apart and becoming a bad guy but he never goes beyond breaking like Walt did. At best, he’s a warning against obsession but he’s still a “good” character.
His greatest failings IIRC are towards Jessie. He has no concern for him but he isn’t allowing himself to cross the line and lie/kill/disgrace himself. He could easily just kill Walt secretly and leave him in the desert but even Walt know Hank isn’t a dirty cop.
He has also "crossed the line" several times. He committed aggravated criminal battery against Jesse, and against a minor drug dealer in a bar for no reason other than to convince himself he wasn't a coward.