In my games, as regards characters with CAKs, they shouldn't even take a chance at killing the opposition (unless provoked or otherwise decide to use lethal force). This is especially so for 20-pointers. You don't even /risk/ killing anyone. That means doing less damage than normal, pulling punches, because if you do accidentally kill someone...
Sure. But only against people who the character knows can take it This means, among other things, voluntarily hitting armour (in the case of armour with an activation roll). A high roll against an unarmoured target can kill, even with a 2d6K attack. And, of course, the BODY rules only really apply to PCs... NPCs, especially grunts, can die long before they reach 0 BODY. This is usually a factor of hit locations, but the GM can rule it any time. And if someone really wants to be careful about not killing, they should take that into account - even if the GM NEVER rules such. It /is/ possible, and only in the most four-colour of four-colour games should it be ignored. And even then, you probably shouldn't be using KAs.
Anyway... for me, a CAK not only includes 'killing,' but also a reluctance to harm innocents. In my games, it goes hand in hand. Some other people may prefer multiple disads. Even Grifter (Image comics), a hardened killer, felt incredibly guilty when a woman got injured by ricochets in a fight that he was involved in. Guilty to the point where he nearly blew the mission to rescue her, take her to hospital, and give her all the money he was getting from the mission. If Superman accidentally injures someone, then the bad guy's getting away - 'cause Supes has to fly someone to the hospital.
A properly responsible hero will take these things into account. If there's any chance of an attack killing someone, they won't use it. Unless, of course, they have a weaker CAK and decide they're gonna kill someone. If there are civilians around, they won't use guns for fear of missing and hitting said bystanders. They won't go 'well, there isn't much chance of me missing, and even if I do miss, they'll only take 7 BODY on average... they'll likely live!' They simply won't take the chance. 'Cause even a 2d6RKA /can/ kill someone... a 6d6EB will hardly ever kill anyone. Even a normal. That's why KAs are KAs - they won't necessarily kill anyone, but, in general, they're much more likely to.
Now, that's not to mean that all heroes will think the same way. Those who don't, though, will often develop a reputation for being a loose cannon, or even dangerous. And, naturally, this is the way I run it in my games - a kind of high superhero, but not all the way to four-colour. Other games will have different moral attitudes. It's one thing that's important to spell out to your players as the game begins.