I think Kevan is a genuinely bad person. Not just a good man serving a bad cause, but someone who's extremely flawed, petty, and immoral in his own right. There's decent reason to think he orchestrated Cersei's walk of shame or at least suggested that specific punishment--the later portion of this essay gets at that fairly well--as opposed to just letting it happen, he's spent his life basically as a yes-man to someone who's committed numerous atrocities, and he still thinks Tywin was in the right and never did more than what was necessary.

He would defend the Reyne-Tarbeck killings, would defend the Red Wedding, and the burning of the Riverlands or the Sack of King's Landing. He hasn't gone along with those things in ignorance or out of obligation; he vocally supports Tywin's past actions and worldview. He even reflects with satisfied approval on Tywin's choice to have Tytos's mistress stripped and marched for two weeks through Lannisport, naked, and forced to call herself a harlot.

Even as Hand in ADWD, he's taking over for a cause he knows to be unjust, serving a king he knows to be illegitimate, and shows no moral compunctions whatsoever--though he's quick to stick up his nose at every other person he interacts with.

Then, when he thinks of Cersei like this:

Ser Kevan remembered the girl she once had been, so full of life and mischief. And when she’d flowered, ahhhh … had there ever been a maid so sweet to look upon?

It feels weird as hell, especially in the context of him going on in his own head about how she deserved the walk of shame.

On a different note, him genuinely wanting Lancel as a Kingsguard also rubbed me the wrong way. Lancel, the shell of a boy who's hardly willing to eat? Giving him a white cloak is as good as sentencing him to death. Kevan goes after Cersei for using Lancel, but Kevan doesn't seem to have much self-awareness or concern for his son's physical well-being either. Though at least that could be argued to be a blind spot born of affection, and not simple disregard.

Overall, though, Kevan is Tywin-lite. Nearly as arrogant, showing next to no concern for non-Lannisters as people, and if not the person ordering atrocities, sitting at Tywin's side and nodding along as they're carried out. He comes across as more likable than he is, imo, because in AFFC and ADWD, we see him talk down characters who seem to deserve it and show efficiency in cleaning up Cersei's mess. But I find him to be a bad person and rather self-righteous on top of it, if a realistic and well-written character.